mirror of
https://github.com/boostorg/math.git
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1072 lines
22 KiB
XML
1072 lines
22 KiB
XML
<?xml version='1.0'?>
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<!DOCTYPE html PUBLIC '-//W3C//DTD XHTML 1.1 plus MathML 2.0//EN'
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'http://www.w3.org/TR/MathML2/dtd/xhtml-math11-f.dtd'
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[<!ENTITY mathml 'http://www.w3.org/1998/Math/MathML'>]>
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<html xmlns='http://www.w3.org/1999/xhtml'>
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<head>
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<!-- MathML created with MathCast Equation Editor version 0.83 -->
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</head>
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<body>
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<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
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<mrow>
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<mtext>hazard</mtext>
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<mfenced>
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<mrow>
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<mi>x</mi>
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</mrow>
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</mfenced>
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<mspace width="1em"/>
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<mo>=</mo>
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<mspace width="1em"/>
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<mi>h</mi>
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<mfenced>
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<mrow>
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<mi>x</mi>
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</mrow>
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</mfenced>
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<mspace width="1em"/>
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<mo>=</mo>
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<mspace width="1em"/>
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<mfrac>
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<mrow>
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<mtext>pdf</mtext>
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<mfenced>
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<mrow>
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<mi>x</mi>
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</mrow>
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</mfenced>
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</mrow>
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<mrow>
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<mn>1</mn>
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<mo>−</mo>
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<mtext>cdf</mtext>
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<mfenced>
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<mrow>
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<mi>x</mi>
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</mrow>
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</mfenced>
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</mrow>
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</mfrac>
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</mrow>
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</math>
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<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
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<mrow>
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<mtext>chf</mtext>
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<mfenced>
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<mrow>
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<mi>d</mi>
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<mi>i</mi>
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<mi>s</mi>
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<mi>t</mi>
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<mo>,</mo>
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<mi>x</mi>
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</mrow>
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</mfenced>
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<mspace width="1em"/>
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<mo>=</mo>
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<mspace width="1em"/>
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<mi>H</mi>
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<mfenced>
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<mrow>
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<mi>x</mi>
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</mrow>
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</mfenced>
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<mspace width="1em"/>
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<mo>=</mo>
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<mspace width="1em"/>
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<munderover>
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<mo>∫</mo>
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<mrow>
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<mo>−</mo>
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<mi>∞</mi>
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</mrow>
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<mi>x</mi>
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</munderover>
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<mi>h</mi>
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<mfenced>
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<mrow>
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<mi>μ</mi>
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</mrow>
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</mfenced>
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<mi>d</mi>
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<mi>μ</mi>
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</mrow>
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</math>
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<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
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<mrow>
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<mi>t</mi>
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<mspace width="1em"/>
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<mo>=</mo>
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<mspace width="1em"/>
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<mfrac>
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<mrow>
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<mi>μ</mi>
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<mo>−</mo>
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<mi>M</mi>
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</mrow>
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<mrow>
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<mfrac>
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<mi>s</mi>
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<msqrt>
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<mi>N</mi>
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</msqrt>
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</mfrac>
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</mrow>
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</mfrac>
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</mrow>
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</math>
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<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
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<mrow>
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<mtable>
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<mtr>
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<mtd>
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<mtext>f</mtext>
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<mfenced>
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<mrow>
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<mi>k</mi>
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<mo>;</mo>
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<mi>n</mi>
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<mo>,</mo>
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<mi>p</mi>
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</mrow>
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</mfenced>
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</mtd>
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<mtd>
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<mo>=</mo>
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</mtd>
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<mtd>
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<msub>
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<mi/>
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<mi>n</mi>
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</msub>
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<msub>
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<mi>C</mi>
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<mi>k</mi>
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</msub>
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<msup>
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<mi>p</mi>
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<mi>k</mi>
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</msup>
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<msup>
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<mfenced>
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<mrow>
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<mn>1</mn>
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<mo>−</mo>
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<mi>p</mi>
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</mrow>
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</mfenced>
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<mrow>
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<mi>n</mi>
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<mo>−</mo>
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<mi>k</mi>
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</mrow>
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</msup>
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</mtd>
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</mtr>
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<mtr>
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<mtd>
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<mspace width="1em"/>
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</mtd>
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<mtd>
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<mo>=</mo>
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</mtd>
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<mtd>
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<mfrac>
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<mrow>
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<mi>n</mi>
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<mo>!</mo>
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</mrow>
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<mrow>
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<mi>k</mi>
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<mo>!</mo>
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<mfenced>
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<mrow>
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<mi>n</mi>
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<mo>−</mo>
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<mi>k</mi>
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</mrow>
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</mfenced>
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<mo>!</mo>
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</mrow>
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</mfrac>
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<msup>
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<mi>p</mi>
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<mi>k</mi>
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</msup>
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<msup>
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<mfenced>
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<mrow>
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<mn>1</mn>
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<mo>−</mo>
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<mi>p</mi>
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</mrow>
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</mfenced>
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<mrow>
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<mi>n</mi>
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<mo>−</mo>
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<mi>k</mi>
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</mrow>
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</msup>
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</mtd>
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</mtr>
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<mtr>
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<mtd>
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<mspace width="1em"/>
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</mtd>
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<mtd>
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<mo>=</mo>
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</mtd>
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<mtd>
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<mfrac>
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<mrow>
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<mi>Γ</mi>
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<mfenced>
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<mrow>
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<mi>n</mi>
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<mo>+</mo>
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<mn>1</mn>
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</mrow>
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</mfenced>
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</mrow>
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<mrow>
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<mi>Γ</mi>
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<mfenced>
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<mrow>
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<mi>k</mi>
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<mo>+</mo>
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<mn>1</mn>
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</mrow>
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</mfenced>
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<mi>Γ</mi>
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<mfenced>
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<mrow>
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<mi>n</mi>
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<mo>−</mo>
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<mi>k</mi>
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<mo>+</mo>
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<mn>1</mn>
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</mrow>
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</mfenced>
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</mrow>
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</mfrac>
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<msup>
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<mi>p</mi>
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<mi>k</mi>
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</msup>
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<msup>
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<mfenced>
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<mrow>
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<mn>1</mn>
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<mo>−</mo>
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<mi>p</mi>
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</mrow>
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</mfenced>
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<mrow>
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<mi>n</mi>
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<mo>−</mo>
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<mi>k</mi>
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</mrow>
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</msup>
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</mtd>
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</mtr>
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<mtr>
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<mtd>
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<mspace width="1em"/>
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</mtd>
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<mtd>
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<mo>=</mo>
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</mtd>
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<mtd>
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<mfrac>
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<mrow>
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<msup>
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<mi>p</mi>
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<mi>k</mi>
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</msup>
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<msup>
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<mfenced>
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<mrow>
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<mn>1</mn>
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<mo>−</mo>
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<mi>p</mi>
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</mrow>
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</mfenced>
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<mrow>
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<mi>n</mi>
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<mo>−</mo>
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<mi>k</mi>
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</mrow>
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</msup>
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</mrow>
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<mrow>
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<mi>B</mi>
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<mfenced>
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<mrow>
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<mi>k</mi>
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<mo>+</mo>
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<mn>1,</mn>
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<mi>n</mi>
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<mo>−</mo>
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<mi>k</mi>
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<mo>+</mo>
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<mn>1</mn>
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</mrow>
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</mfenced>
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<mfenced>
|
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<mrow>
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<mi>n</mi>
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<mo>+</mo>
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<mn>1</mn>
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</mrow>
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</mfenced>
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</mrow>
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</mfrac>
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</mtd>
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</mtr>
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</mtable>
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</mrow>
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</math>
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<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
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<mrow>
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<mtable>
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<mtr>
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<mtd>
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<mtext>f</mtext>
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<mfenced>
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<mrow>
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<mi>k</mi>
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<mo>;</mo>
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<mi>n</mi>
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<mo>,</mo>
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<mi>p</mi>
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</mrow>
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</mfenced>
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</mtd>
|
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<mtd>
|
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<mo>=</mo>
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</mtd>
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<mtd>
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<msub>
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<mi/>
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<mi>n</mi>
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</msub>
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<msub>
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<mi>C</mi>
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<mi>k</mi>
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</msub>
|
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<msup>
|
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<mi>p</mi>
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<mi>k</mi>
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</msup>
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<msup>
|
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<mfenced>
|
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<mrow>
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<mn>1</mn>
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<mo>−</mo>
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<mi>p</mi>
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</mrow>
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</mfenced>
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<mrow>
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<mi>n</mi>
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<mo>−</mo>
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<mi>k</mi>
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</mrow>
|
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</msup>
|
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</mtd>
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</mtr>
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<mtr>
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<mtd>
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<mspace width="1em"/>
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</mtd>
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<mtd>
|
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<mo>=</mo>
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</mtd>
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<mtd>
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<mfrac>
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<mrow>
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<mi>n</mi>
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<mo>!</mo>
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</mrow>
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<mrow>
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<mi>k</mi>
|
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<mo>!</mo>
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<mfenced>
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<mrow>
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<mi>n</mi>
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<mo>−</mo>
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<mi>k</mi>
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</mrow>
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</mfenced>
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<mo>!</mo>
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</mrow>
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</mfrac>
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<msup>
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<mi>p</mi>
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<mi>k</mi>
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</msup>
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<msup>
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<mfenced>
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<mrow>
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<mn>1</mn>
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<mo>−</mo>
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<mi>p</mi>
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</mrow>
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</mfenced>
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<mrow>
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<mi>n</mi>
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<mo>−</mo>
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<mi>k</mi>
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</mrow>
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</msup>
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</mtd>
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</mtr>
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</mtable>
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</mrow>
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</math>
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<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
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<mrow>
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<mtext>f</mtext>
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<mfenced>
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<mrow>
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<mi>x</mi>
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<mo>;</mo>
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<msub>
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<mi>x</mi>
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<mn>0,</mn>
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</msub>
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<mi>γ</mi>
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</mrow>
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</mfenced>
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<mspace width="1em"/>
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<mo>=</mo>
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<mspace width="1em"/>
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<mfrac>
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<mn>1</mn>
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<mi>π</mi>
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</mfrac>
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<mfenced>
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<mrow>
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<mfrac>
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<mi>γ</mi>
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<mrow>
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<msup>
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<mfenced>
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<mrow>
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<mi>x</mi>
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<mo>−</mo>
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<msub>
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<mi>x</mi>
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<mn>0</mn>
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</msub>
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</mrow>
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</mfenced>
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<mn>2</mn>
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</msup>
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<mo>+</mo>
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<msup>
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<mi>γ</mi>
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<mn>2</mn>
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</msup>
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</mrow>
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</mfrac>
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</mrow>
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</mfenced>
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</mrow>
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</math>
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<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
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<mrow>
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<mi>Q</mi>
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<mspace width="1em"/>
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<mo>=</mo>
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<mspace width="1em"/>
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<munderover>
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<mo>∑</mo>
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<mrow>
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<mi>i</mi>
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<mo>=</mo>
|
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<mn>1</mn>
|
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</mrow>
|
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<mi>ν</mi>
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</munderover>
|
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<msup>
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<mfenced>
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<mrow>
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<mfrac>
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<mrow>
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<msub>
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<mi>χ</mi>
|
|
<mi>i</mi>
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</msub>
|
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<mo>−</mo>
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<msub>
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<mi>ν</mi>
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<mi>i</mi>
|
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</msub>
|
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</mrow>
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<mrow>
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<msub>
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<mi>σ</mi>
|
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<mi>i</mi>
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</msub>
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</mrow>
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</mfrac>
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</mrow>
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</mfenced>
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<mn>2</mn>
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</msup>
|
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</mrow>
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</math>
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<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
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<mrow>
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<mi>f</mi>
|
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<mfenced>
|
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<mrow>
|
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<mi>x</mi>
|
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</mrow>
|
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</mfenced>
|
|
<mspace width="1em"/>
|
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<mo>=</mo>
|
|
<mspace width="1em"/>
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|
<mi>λ</mi>
|
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<msup>
|
|
<mi>e</mi>
|
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<mrow>
|
|
<mo>−</mo>
|
|
<mi>λ</mi>
|
|
<mi>x</mi>
|
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</mrow>
|
|
</msup>
|
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</mrow>
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</math>
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<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
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<mrow>
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<mtext>f</mtext>
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<mfenced>
|
|
<mrow>
|
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<mi>x</mi>
|
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</mrow>
|
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</mfenced>
|
|
<mspace width="1em"/>
|
|
<mo>=</mo>
|
|
<mspace width="1em"/>
|
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<mfrac>
|
|
<mn>1</mn>
|
|
<mrow>
|
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<mi>x</mi>
|
|
<mi>s</mi>
|
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<msqrt>
|
|
<mrow>
|
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<mn>2</mn>
|
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<mi>π</mi>
|
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</mrow>
|
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</msqrt>
|
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</mrow>
|
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</mfrac>
|
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<msup>
|
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<mi>e</mi>
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<mrow>
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<mfrac>
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<mrow>
|
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<mo>−</mo>
|
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<msup>
|
|
<mfenced>
|
|
<mrow>
|
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<mi>ln</mi>
|
|
<mi>x</mi>
|
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<mo>−</mo>
|
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<mi>m</mi>
|
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</mrow>
|
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</mfenced>
|
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<mn>2</mn>
|
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</msup>
|
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</mrow>
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<mrow>
|
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<mn>2</mn>
|
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<msup>
|
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<mi>s</mi>
|
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<mn>2</mn>
|
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</msup>
|
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</mrow>
|
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</mfrac>
|
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</mrow>
|
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</msup>
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</mrow>
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</math>
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<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
|
|
<mrow>
|
|
<msub>
|
|
<mtext>f</mtext>
|
|
<mrow>
|
|
<mi>n</mi>
|
|
<mo>,</mo>
|
|
<mi>m</mi>
|
|
</mrow>
|
|
</msub>
|
|
<mfenced>
|
|
<mrow>
|
|
<mi>x</mi>
|
|
</mrow>
|
|
</mfenced>
|
|
<mspace width="1em"/>
|
|
<mo>=</mo>
|
|
<mspace width="1em"/>
|
|
<mfrac>
|
|
<mrow>
|
|
<msup>
|
|
<mi>m</mi>
|
|
<mrow>
|
|
<mfrac>
|
|
<mi>m</mi>
|
|
<mn>2</mn>
|
|
</mfrac>
|
|
</mrow>
|
|
</msup>
|
|
<msup>
|
|
<mi>n</mi>
|
|
<mrow>
|
|
<mfrac>
|
|
<mi>n</mi>
|
|
<mn>2</mn>
|
|
</mfrac>
|
|
</mrow>
|
|
</msup>
|
|
<msup>
|
|
<mi>x</mi>
|
|
<mrow>
|
|
<mfrac>
|
|
<mi>n</mi>
|
|
<mn>2</mn>
|
|
</mfrac>
|
|
<mo>−</mo>
|
|
<mn>1</mn>
|
|
</mrow>
|
|
</msup>
|
|
</mrow>
|
|
<mrow>
|
|
<msup>
|
|
<mfenced>
|
|
<mrow>
|
|
<mi>m</mi>
|
|
<mo>+</mo>
|
|
<mi>n</mi>
|
|
<mi>x</mi>
|
|
</mrow>
|
|
</mfenced>
|
|
<mrow>
|
|
<mfrac>
|
|
<mfenced>
|
|
<mrow>
|
|
<mi>n</mi>
|
|
<mo>+</mo>
|
|
<mi>m</mi>
|
|
</mrow>
|
|
</mfenced>
|
|
<mn>2</mn>
|
|
</mfrac>
|
|
</mrow>
|
|
</msup>
|
|
<mi>B</mi>
|
|
<mfenced>
|
|
<mrow>
|
|
<mfrac>
|
|
<mi>n</mi>
|
|
<mn>2,</mn>
|
|
</mfrac>
|
|
<mfrac>
|
|
<mi>m</mi>
|
|
<mn>2</mn>
|
|
</mfrac>
|
|
</mrow>
|
|
</mfenced>
|
|
</mrow>
|
|
</mfrac>
|
|
</mrow>
|
|
</math>
|
|
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
|
|
<mrow>
|
|
<mtext>f</mtext>
|
|
<mfenced>
|
|
<mrow>
|
|
<mi>x</mi>
|
|
<mo>;</mo>
|
|
<mi>μ</mi>
|
|
<mo>,</mo>
|
|
<mi>σ</mi>
|
|
</mrow>
|
|
</mfenced>
|
|
<mspace width="1em"/>
|
|
<mo>=</mo>
|
|
<mspace width="1em"/>
|
|
<mfrac>
|
|
<mn>1</mn>
|
|
<mrow>
|
|
<mi>σ</mi>
|
|
<msqrt>
|
|
<mrow>
|
|
<mn>2</mn>
|
|
<mi>π</mi>
|
|
</mrow>
|
|
</msqrt>
|
|
</mrow>
|
|
</mfrac>
|
|
<msup>
|
|
<mi>e</mi>
|
|
<mrow>
|
|
<mo>−</mo>
|
|
<mfrac>
|
|
<mrow>
|
|
<msup>
|
|
<mfenced>
|
|
<mrow>
|
|
<mi>x</mi>
|
|
<mo>−</mo>
|
|
<mi>μ</mi>
|
|
</mrow>
|
|
</mfenced>
|
|
<mn>2</mn>
|
|
</msup>
|
|
</mrow>
|
|
<mrow>
|
|
<mn>2</mn>
|
|
<msup>
|
|
<mi>σ</mi>
|
|
<mn>2</mn>
|
|
</msup>
|
|
</mrow>
|
|
</mfrac>
|
|
</mrow>
|
|
</msup>
|
|
</mrow>
|
|
</math>
|
|
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
|
|
<mrow>
|
|
<mtext>f</mtext>
|
|
<mfenced>
|
|
<mrow>
|
|
<mi>k</mi>
|
|
<mo>;</mo>
|
|
<mi>λ</mi>
|
|
</mrow>
|
|
</mfenced>
|
|
<mspace width="1em"/>
|
|
<mo>=</mo>
|
|
<mspace width="1em"/>
|
|
<mfrac>
|
|
<mrow>
|
|
<msup>
|
|
<mi>e</mi>
|
|
<mrow>
|
|
<mo>−</mo>
|
|
<mi>λ</mi>
|
|
</mrow>
|
|
</msup>
|
|
<msup>
|
|
<mi>λ</mi>
|
|
<mi>k</mi>
|
|
</msup>
|
|
</mrow>
|
|
<mrow>
|
|
<mi>k</mi>
|
|
<mo>!</mo>
|
|
</mrow>
|
|
</mfrac>
|
|
</mrow>
|
|
</math>
|
|
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
|
|
<mrow>
|
|
<mtext>f</mtext>
|
|
<mfenced>
|
|
<mrow>
|
|
<mi>x</mi>
|
|
</mrow>
|
|
</mfenced>
|
|
<mspace width="1em"/>
|
|
<mo>=</mo>
|
|
<mspace width="1em"/>
|
|
<mfrac>
|
|
<mrow>
|
|
<mi>Γ</mi>
|
|
<mfenced>
|
|
<mrow>
|
|
<mfrac>
|
|
<mrow>
|
|
<mi>ν</mi>
|
|
<mo>+</mo>
|
|
<mn>1</mn>
|
|
</mrow>
|
|
<mn>2</mn>
|
|
</mfrac>
|
|
</mrow>
|
|
</mfenced>
|
|
</mrow>
|
|
<mrow>
|
|
<msqrt>
|
|
<mrow>
|
|
<mi>ν</mi>
|
|
<mi>π</mi>
|
|
</mrow>
|
|
</msqrt>
|
|
<mi>Γ</mi>
|
|
<mfenced>
|
|
<mrow>
|
|
<mfrac>
|
|
<mi>ν</mi>
|
|
<mn>2</mn>
|
|
</mfrac>
|
|
</mrow>
|
|
</mfenced>
|
|
<msup>
|
|
<mfenced>
|
|
<mrow>
|
|
<mn>1</mn>
|
|
<mo>+</mo>
|
|
<mfrac>
|
|
<mrow>
|
|
<msup>
|
|
<mi>x</mi>
|
|
<mn>2</mn>
|
|
</msup>
|
|
</mrow>
|
|
<mi>ν</mi>
|
|
</mfrac>
|
|
</mrow>
|
|
</mfenced>
|
|
<mrow>
|
|
<mfrac>
|
|
<mrow>
|
|
<mi>ν</mi>
|
|
<mo>+</mo>
|
|
<mn>1</mn>
|
|
</mrow>
|
|
<mn>2</mn>
|
|
</mfrac>
|
|
</mrow>
|
|
</msup>
|
|
</mrow>
|
|
</mfrac>
|
|
</mrow>
|
|
</math>
|
|
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
|
|
<mrow>
|
|
<mtext>f</mtext>
|
|
<mfenced>
|
|
<mrow>
|
|
<mi>x</mi>
|
|
<mo>;</mo>
|
|
<mi>k</mi>
|
|
<mo>,</mo>
|
|
<mi>θ</mi>
|
|
</mrow>
|
|
</mfenced>
|
|
<mspace width="1em"/>
|
|
<mo>=</mo>
|
|
<mspace width="1em"/>
|
|
<msup>
|
|
<mi>x</mi>
|
|
<mrow>
|
|
<mi>k</mi>
|
|
<mo>−</mo>
|
|
<mn>1</mn>
|
|
</mrow>
|
|
</msup>
|
|
<mfrac>
|
|
<msup>
|
|
<mi>e</mi>
|
|
<mrow>
|
|
<mo>−</mo>
|
|
<mfrac>
|
|
<mi>x</mi>
|
|
<mi>θ</mi>
|
|
</mfrac>
|
|
</mrow>
|
|
</msup>
|
|
<mrow>
|
|
<msup>
|
|
<mi>θ</mi>
|
|
<mi>k</mi>
|
|
</msup>
|
|
<mi>Γ</mi>
|
|
<mfenced>
|
|
<mrow>
|
|
<mi>k</mi>
|
|
</mrow>
|
|
</mfenced>
|
|
</mrow>
|
|
</mfrac>
|
|
</mrow>
|
|
</math>
|
|
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
|
|
<mrow>
|
|
<mtext>f</mtext>
|
|
<mfenced>
|
|
<mrow>
|
|
<mi>x</mi>
|
|
<mo>;</mo>
|
|
<mi>α</mi>
|
|
<mo>,</mo>
|
|
<mi>β</mi>
|
|
</mrow>
|
|
</mfenced>
|
|
<mspace width="1em"/>
|
|
<mo>=</mo>
|
|
<mspace width="1em"/>
|
|
<msup>
|
|
<mi>x</mi>
|
|
<mrow>
|
|
<mi>α</mi>
|
|
<mo>−</mo>
|
|
<mn>1</mn>
|
|
</mrow>
|
|
</msup>
|
|
<mfrac>
|
|
<mrow>
|
|
<msup>
|
|
<mi>β</mi>
|
|
<mi>α</mi>
|
|
</msup>
|
|
<msup>
|
|
<mi>e</mi>
|
|
<mrow>
|
|
<mo>−</mo>
|
|
<mi>β</mi>
|
|
<mi>x</mi>
|
|
</mrow>
|
|
</msup>
|
|
</mrow>
|
|
<mrow>
|
|
<mi>Γ</mi>
|
|
<mfenced>
|
|
<mrow>
|
|
<mi>α</mi>
|
|
</mrow>
|
|
</mfenced>
|
|
</mrow>
|
|
</mfrac>
|
|
</mrow>
|
|
</math>
|
|
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
|
|
<mrow>
|
|
<mi>f</mi>
|
|
<mfenced>
|
|
<mrow>
|
|
<mi>k</mi>
|
|
<mo>;</mo>
|
|
<mi>r</mi>
|
|
<mo>,</mo>
|
|
<mi>p</mi>
|
|
</mrow>
|
|
</mfenced>
|
|
<mspace width="1em"/>
|
|
<mo>=</mo>
|
|
<mspace width="1em"/>
|
|
<mfrac>
|
|
<mrow>
|
|
<mi>Γ</mi>
|
|
<mfenced>
|
|
<mrow>
|
|
<mi>r</mi>
|
|
<mo>+</mo>
|
|
<mi>k</mi>
|
|
</mrow>
|
|
</mfenced>
|
|
</mrow>
|
|
<mrow>
|
|
<mi>k</mi>
|
|
<mo>!</mo>
|
|
<mi>Γ</mi>
|
|
<mfenced>
|
|
<mrow>
|
|
<mi>r</mi>
|
|
</mrow>
|
|
</mfenced>
|
|
</mrow>
|
|
</mfrac>
|
|
<msup>
|
|
<mi>p</mi>
|
|
<mi>r</mi>
|
|
</msup>
|
|
<msup>
|
|
<mfenced>
|
|
<mrow>
|
|
<mn>1</mn>
|
|
<mo>−</mo>
|
|
<mi>p</mi>
|
|
</mrow>
|
|
</mfenced>
|
|
<mi>k</mi>
|
|
</msup>
|
|
</mrow>
|
|
</math>
|
|
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
|
|
<mrow>
|
|
<mn>6</mn>
|
|
<mfrac>
|
|
<mrow>
|
|
<msup>
|
|
<mi>α</mi>
|
|
<mn>3</mn>
|
|
</msup>
|
|
<mo>−</mo>
|
|
<msup>
|
|
<mi>α</mi>
|
|
<mn>2</mn>
|
|
</msup>
|
|
<mfenced>
|
|
<mrow>
|
|
<mn>2</mn>
|
|
<mi>β</mi>
|
|
<mo>−</mo>
|
|
<mn>1</mn>
|
|
</mrow>
|
|
</mfenced>
|
|
<mo>+</mo>
|
|
<msup>
|
|
<mi>β</mi>
|
|
<mn>2</mn>
|
|
</msup>
|
|
<mfenced>
|
|
<mrow>
|
|
<mi>β</mi>
|
|
<mo>−</mo>
|
|
<mn>1</mn>
|
|
</mrow>
|
|
</mfenced>
|
|
<mo>−</mo>
|
|
<mn>2</mn>
|
|
<mi>α</mi>
|
|
<mi>β</mi>
|
|
<mfenced>
|
|
<mrow>
|
|
<mi>β</mi>
|
|
<mo>+</mo>
|
|
<mn>2</mn>
|
|
</mrow>
|
|
</mfenced>
|
|
</mrow>
|
|
<mrow>
|
|
<mi>α</mi>
|
|
<mi>β</mi>
|
|
<mfenced>
|
|
<mrow>
|
|
<mi>α</mi>
|
|
<mo>+</mo>
|
|
<mi>β</mi>
|
|
<mo>+</mo>
|
|
<mn>2</mn>
|
|
</mrow>
|
|
</mfenced>
|
|
<mfenced>
|
|
<mrow>
|
|
<mi>α</mi>
|
|
<mo>+</mo>
|
|
<mi>β</mi>
|
|
<mo>+</mo>
|
|
<mn>3</mn>
|
|
</mrow>
|
|
</mfenced>
|
|
</mrow>
|
|
</mfrac>
|
|
</mrow>
|
|
</math>
|
|
</body>
|
|
</html> |