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https://github.com/boostorg/math.git
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1076 lines
20 KiB
XML
1076 lines
20 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>tgamma</mtext>
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<mfenced>
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<mrow>
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<mi>a</mi>
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<mo>,</mo>
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<mi>z</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>Γ</mi>
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<mfenced>
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<mrow>
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<mi>a</mi>
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<mo>,</mo>
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<mi>z</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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<mi>z</mi>
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</mrow>
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<mi>∞</mi>
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</munderover>
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<msup>
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<mi>t</mi>
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<mrow>
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<mi>a</mi>
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<mo>−</mo>
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<mn>1</mn>
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</mrow>
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</msup>
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<msup>
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<mi>e</mi>
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<mrow>
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<mo>−</mo>
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<mi>t</mi>
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</mrow>
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</msup>
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<mi>d</mi>
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<mi>t</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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<mtext>tgamma_lower</mtext>
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<mfenced>
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<mrow>
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<mi>a</mi>
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<mo>,</mo>
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<mi>z</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>γ</mi>
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<mfenced>
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<mrow>
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<mi>a</mi>
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<mo>,</mo>
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<mi>z</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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<mn>0</mn>
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</mrow>
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<mi>z</mi>
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</munderover>
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<msup>
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<mi>t</mi>
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<mrow>
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<mi>a</mi>
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<mo>−</mo>
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<mn>1</mn>
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</mrow>
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</msup>
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<msup>
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<mi>e</mi>
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<mrow>
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<mo>−</mo>
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<mi>t</mi>
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</mrow>
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</msup>
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<mi>d</mi>
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<mi>t</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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<mtext>gamma_Q</mtext>
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<mfenced>
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<mrow>
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<mi>a</mi>
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<mo>,</mo>
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<mi>z</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>Q</mi>
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<mfenced>
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<mrow>
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<mi>a</mi>
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<mo>,</mo>
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<mi>z</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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<mi>Γ</mi>
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<mfenced>
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<mrow>
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<mi>a</mi>
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<mo>,</mo>
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<mi>z</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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<mi>Γ</mi>
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<mfenced>
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<mrow>
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<mi>a</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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<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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<mrow>
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<mi>Γ</mi>
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<mfenced>
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<mrow>
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<mi>a</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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<munderover>
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<mo>∫</mo>
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<mrow>
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<mi>z</mi>
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</mrow>
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<mi>∞</mi>
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</munderover>
|
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<msup>
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<mi>t</mi>
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<mrow>
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<mi>a</mi>
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<mo>−</mo>
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<mn>1</mn>
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</mrow>
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</msup>
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<msup>
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<mi>e</mi>
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<mrow>
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<mo>−</mo>
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<mi>t</mi>
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</mrow>
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</msup>
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<mi>d</mi>
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<mi>t</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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<mtext>gamma_P</mtext>
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<mfenced>
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<mrow>
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<mi>a</mi>
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<mo>,</mo>
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<mi>z</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>P</mi>
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<mfenced>
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<mrow>
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<mi>a</mi>
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<mo>,</mo>
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<mi>z</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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<mi>γ</mi>
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<mfenced>
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<mrow>
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<mi>a</mi>
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<mo>,</mo>
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<mi>z</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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<mi>Γ</mi>
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<mfenced>
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<mrow>
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<mi>a</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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<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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<mrow>
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<mi>Γ</mi>
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<mfenced>
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<mrow>
|
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<mi>a</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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<munderover>
|
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<mo>∫</mo>
|
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<mrow>
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<mn>0</mn>
|
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</mrow>
|
|
<mi>z</mi>
|
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</munderover>
|
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<msup>
|
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<mi>t</mi>
|
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<mrow>
|
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<mi>a</mi>
|
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<mo>−</mo>
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<mn>1</mn>
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</mrow>
|
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</msup>
|
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<msup>
|
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<mi>e</mi>
|
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<mrow>
|
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<mo>−</mo>
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<mi>t</mi>
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</mrow>
|
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</msup>
|
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<mi>d</mi>
|
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<mi>t</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>Q</mi>
|
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<mfenced>
|
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<mrow>
|
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<mi>a</mi>
|
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<mo>,</mo>
|
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<mi>x</mi>
|
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</mrow>
|
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</mfenced>
|
|
<mo>+</mo>
|
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<mi>P</mi>
|
|
<mfenced>
|
|
<mrow>
|
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<mi>a</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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<mn>1</mn>
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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>Γ</mi>
|
|
<mfenced>
|
|
<mrow>
|
|
<mi>a</mi>
|
|
<mo>,</mo>
|
|
<mi>z</mi>
|
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</mrow>
|
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</mfenced>
|
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<mo>+</mo>
|
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<mi>γ</mi>
|
|
<mfenced>
|
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<mrow>
|
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<mi>a</mi>
|
|
<mo>,</mo>
|
|
<mi>z</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>Γ</mi>
|
|
<mfenced>
|
|
<mrow>
|
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<mi>a</mi>
|
|
</mrow>
|
|
</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>
|
|
<mi>Q</mi>
|
|
<mfenced>
|
|
<mrow>
|
|
<mi>a</mi>
|
|
<mo>,</mo>
|
|
<mi>z</mi>
|
|
</mrow>
|
|
</mfenced>
|
|
<mspace width="1em"/>
|
|
<mo>=</mo>
|
|
<mspace width="1em"/>
|
|
<mfrac>
|
|
<mrow>
|
|
<mi>Γ</mi>
|
|
<mfenced>
|
|
<mrow>
|
|
<mi>a</mi>
|
|
<mo>,</mo>
|
|
<mi>z</mi>
|
|
</mrow>
|
|
</mfenced>
|
|
</mrow>
|
|
<mrow>
|
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<mi>Γ</mi>
|
|
<mfenced>
|
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<mrow>
|
|
<mi>a</mi>
|
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</mrow>
|
|
</mfenced>
|
|
</mrow>
|
|
</mfrac>
|
|
<mspace width="1em"/>
|
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<mo>,</mo>
|
|
<mspace width="1em"/>
|
|
<mi>P</mi>
|
|
<mfenced>
|
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<mrow>
|
|
<mi>a</mi>
|
|
<mo>,</mo>
|
|
<mi>z</mi>
|
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</mrow>
|
|
</mfenced>
|
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<mspace width="1em"/>
|
|
<mo>=</mo>
|
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<mspace width="1em"/>
|
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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>a</mi>
|
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<mo>,</mo>
|
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<mi>z</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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<mi>Γ</mi>
|
|
<mfenced>
|
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<mrow>
|
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<mi>a</mi>
|
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</mrow>
|
|
</mfenced>
|
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</mrow>
|
|
</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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<mi>γ</mi>
|
|
<mfenced>
|
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<mrow>
|
|
<mi>a</mi>
|
|
<mo>,</mo>
|
|
<mi>x</mi>
|
|
</mrow>
|
|
</mfenced>
|
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<mspace width="1em"/>
|
|
<mo>=</mo>
|
|
<mspace width="1em"/>
|
|
<msup>
|
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<mi>x</mi>
|
|
<mi>a</mi>
|
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</msup>
|
|
<msup>
|
|
<mi>e</mi>
|
|
<mrow>
|
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<mo>−</mo>
|
|
<mi>x</mi>
|
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</mrow>
|
|
</msup>
|
|
<munderover>
|
|
<mo>∑</mo>
|
|
<mrow>
|
|
<mi>k</mi>
|
|
<mo>=</mo>
|
|
<mn>0</mn>
|
|
</mrow>
|
|
<mi>∞</mi>
|
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</munderover>
|
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<mrow>
|
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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>a</mi>
|
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</mrow>
|
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</mfenced>
|
|
</mrow>
|
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<mrow>
|
|
<mi>Γ</mi>
|
|
<mfenced>
|
|
<mrow>
|
|
<mi>a</mi>
|
|
<mo>+</mo>
|
|
<mi>k</mi>
|
|
<mo>+</mo>
|
|
<mn>1</mn>
|
|
</mrow>
|
|
</mfenced>
|
|
</mrow>
|
|
</mfrac>
|
|
</mrow>
|
|
<msup>
|
|
<mi>x</mi>
|
|
<mi>n</mi>
|
|
</msup>
|
|
<mspace width="1em"/>
|
|
<mo>=</mo>
|
|
<mspace width="1em"/>
|
|
<msup>
|
|
<mi>x</mi>
|
|
<mi>a</mi>
|
|
</msup>
|
|
<msup>
|
|
<mi>e</mi>
|
|
<mrow>
|
|
<mo>−</mo>
|
|
<mi>x</mi>
|
|
</mrow>
|
|
</msup>
|
|
<munderover>
|
|
<mo>∑</mo>
|
|
<mrow>
|
|
<mi>k</mi>
|
|
<mo>=</mo>
|
|
<mn>0</mn>
|
|
</mrow>
|
|
<mi>∞</mi>
|
|
</munderover>
|
|
<mfrac>
|
|
<mrow>
|
|
<msup>
|
|
<mi>x</mi>
|
|
<mi>n</mi>
|
|
</msup>
|
|
</mrow>
|
|
<mrow>
|
|
<msup>
|
|
<mi>a</mi>
|
|
<mover>
|
|
<mrow>
|
|
<mi>k</mi>
|
|
<mo>+</mo>
|
|
<mn>1</mn>
|
|
</mrow>
|
|
<mo>−</mo>
|
|
</mover>
|
|
</msup>
|
|
</mrow>
|
|
</mfrac>
|
|
</mrow>
|
|
</math>
|
|
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
|
|
<mrow>
|
|
<mi>Γ</mi>
|
|
<mfenced>
|
|
<mrow>
|
|
<mi>a</mi>
|
|
<mo>,</mo>
|
|
<mi>z</mi>
|
|
</mrow>
|
|
</mfenced>
|
|
<mspace width="1em"/>
|
|
<mo>=</mo>
|
|
<mspace width="1em"/>
|
|
<mfrac>
|
|
<mrow>
|
|
<msup>
|
|
<mi>x</mi>
|
|
<mi>a</mi>
|
|
</msup>
|
|
<msup>
|
|
<mi>e</mi>
|
|
<mrow>
|
|
<mo>−</mo>
|
|
<mi>x</mi>
|
|
</mrow>
|
|
</msup>
|
|
</mrow>
|
|
<mrow>
|
|
<mi>x</mi>
|
|
<mo>−</mo>
|
|
<mi>a</mi>
|
|
<mo>+</mo>
|
|
<mn>1</mn>
|
|
<mo>+</mo>
|
|
<mfrac>
|
|
<mrow>
|
|
<msub>
|
|
<mi>a</mi>
|
|
<mi>k</mi>
|
|
</msub>
|
|
</mrow>
|
|
<mrow>
|
|
<msub>
|
|
<mi>b</mi>
|
|
<mi>k</mi>
|
|
</msub>
|
|
<mo>+</mo>
|
|
<mfrac>
|
|
<mrow>
|
|
<msub>
|
|
<mi>a</mi>
|
|
<mrow>
|
|
<mi>k</mi>
|
|
<mo>+</mo>
|
|
<mn>1</mn>
|
|
</mrow>
|
|
</msub>
|
|
</mrow>
|
|
<mrow>
|
|
<msub>
|
|
<mi>b</mi>
|
|
<mrow>
|
|
<mi>k</mi>
|
|
<mo>+</mo>
|
|
<mn>1</mn>
|
|
</mrow>
|
|
</msub>
|
|
<mo>+</mo>
|
|
<mo>…</mo>
|
|
</mrow>
|
|
</mfrac>
|
|
</mrow>
|
|
</mfrac>
|
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</mrow>
|
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</mfrac>
|
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<mspace width="1em"/>
|
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<mo>;</mo>
|
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<mspace width="1em"/>
|
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<msub>
|
|
<mi>a</mi>
|
|
<mi>k</mi>
|
|
</msub>
|
|
<mo>=</mo>
|
|
<mi>k</mi>
|
|
<mfenced>
|
|
<mrow>
|
|
<mi>a</mi>
|
|
<mo>-</mo>
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|
<mi>k</mi>
|
|
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|
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|
<mspace width="1em"/>
|
|
<mo>;</mo>
|
|
<mspace width="1em"/>
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<msub>
|
|
<mi>b</mi>
|
|
<mi>k</mi>
|
|
</msub>
|
|
<mo>=</mo>
|
|
<mi>x</mi>
|
|
<mo>−</mo>
|
|
<mi>a</mi>
|
|
<mo>+</mo>
|
|
<mn>2</mn>
|
|
<mi>k</mi>
|
|
<mo>+</mo>
|
|
<mn>1</mn>
|
|
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|
|
</math>
|
|
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
|
|
<mrow>
|
|
<mi>γ</mi>
|
|
<mfenced>
|
|
<mrow>
|
|
<mi>a</mi>
|
|
<mo>,</mo>
|
|
<mi>x</mi>
|
|
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|
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|
<mspace width="1em"/>
|
|
<mo>=</mo>
|
|
<mspace width="1em"/>
|
|
<msup>
|
|
<mi>x</mi>
|
|
<mi>a</mi>
|
|
</msup>
|
|
<munderover>
|
|
<mo>∑</mo>
|
|
<mrow>
|
|
<mi>k</mi>
|
|
<mo>=</mo>
|
|
<mn>0</mn>
|
|
</mrow>
|
|
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|
|
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|
|
<mfrac>
|
|
<mrow>
|
|
<msup>
|
|
<mfenced>
|
|
<mrow>
|
|
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|
|
<mn>1</mn>
|
|
</mrow>
|
|
</mfenced>
|
|
<mi>k</mi>
|
|
</msup>
|
|
<msup>
|
|
<mi>x</mi>
|
|
<mi>k</mi>
|
|
</msup>
|
|
</mrow>
|
|
<mrow>
|
|
<mfenced>
|
|
<mrow>
|
|
<mi>a</mi>
|
|
<mo>+</mo>
|
|
<mi>k</mi>
|
|
</mrow>
|
|
</mfenced>
|
|
<mi>k</mi>
|
|
<mo>!</mo>
|
|
</mrow>
|
|
</mfrac>
|
|
</mrow>
|
|
</math>
|
|
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
|
|
<mrow>
|
|
<mi>Γ</mi>
|
|
<mfenced>
|
|
<mrow>
|
|
<mi>a</mi>
|
|
<mo>,</mo>
|
|
<mi>x</mi>
|
|
</mrow>
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|
</mfenced>
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|
<mspace width="1em"/>
|
|
<mo>=</mo>
|
|
<mspace width="1em"/>
|
|
<mfrac>
|
|
<mrow>
|
|
<mtext>gp1m1</mtext>
|
|
<mfenced>
|
|
<mrow>
|
|
<mi>a</mi>
|
|
</mrow>
|
|
</mfenced>
|
|
<mo>−</mo>
|
|
<mtext>powm1</mtext>
|
|
<mfenced>
|
|
<mrow>
|
|
<mi>x</mi>
|
|
<mo>,</mo>
|
|
<mi>a</mi>
|
|
</mrow>
|
|
</mfenced>
|
|
</mrow>
|
|
<mi>a</mi>
|
|
</mfrac>
|
|
<mo>+</mo>
|
|
<msup>
|
|
<mi>x</mi>
|
|
<mi>a</mi>
|
|
</msup>
|
|
<munderover>
|
|
<mo>∑</mo>
|
|
<mrow>
|
|
<mi>k</mi>
|
|
<mo>=</mo>
|
|
<mn>1</mn>
|
|
</mrow>
|
|
<mi>∞</mi>
|
|
</munderover>
|
|
<mfrac>
|
|
<mrow>
|
|
<msup>
|
|
<mfenced>
|
|
<mrow>
|
|
<mo>−</mo>
|
|
<mn>1</mn>
|
|
</mrow>
|
|
</mfenced>
|
|
<mi>k</mi>
|
|
</msup>
|
|
<msup>
|
|
<mi>x</mi>
|
|
<mi>k</mi>
|
|
</msup>
|
|
</mrow>
|
|
<mrow>
|
|
<mfenced>
|
|
<mrow>
|
|
<mi>a</mi>
|
|
<mo>+</mo>
|
|
<mi>k</mi>
|
|
</mrow>
|
|
</mfenced>
|
|
<mi>k</mi>
|
|
<mo>!</mo>
|
|
</mrow>
|
|
</mfrac>
|
|
<mspace width="1em"/>
|
|
<mo>;</mo>
|
|
<mspace width="1em"/>
|
|
<mtext>gp1m1</mtext>
|
|
<mfenced>
|
|
<mrow>
|
|
<mi>a</mi>
|
|
</mrow>
|
|
</mfenced>
|
|
<mo>=</mo>
|
|
<mi>Γ</mi>
|
|
<mfenced>
|
|
<mrow>
|
|
<mi>a</mi>
|
|
<mo>+</mo>
|
|
<mn>1</mn>
|
|
</mrow>
|
|
</mfenced>
|
|
<mo>−</mo>
|
|
<mn>1</mn>
|
|
<mspace width="1em"/>
|
|
<mo>∧</mo>
|
|
<mspace width="1em"/>
|
|
<mtext>powm1</mtext>
|
|
<mfenced>
|
|
<mrow>
|
|
<mi>x</mi>
|
|
<mo>,</mo>
|
|
<mi>a</mi>
|
|
</mrow>
|
|
</mfenced>
|
|
<mo>=</mo>
|
|
<msup>
|
|
<mi>x</mi>
|
|
<mi>a</mi>
|
|
</msup>
|
|
<mo>−</mo>
|
|
<mn>1</mn>
|
|
</mrow>
|
|
</math>
|
|
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
|
|
<mrow>
|
|
<mfrac>
|
|
<mrow>
|
|
<msup>
|
|
<mi>x</mi>
|
|
<mi>a</mi>
|
|
</msup>
|
|
<msup>
|
|
<mi>e</mi>
|
|
<mrow>
|
|
<mo>−</mo>
|
|
<mi>x</mi>
|
|
</mrow>
|
|
</msup>
|
|
</mrow>
|
|
<mrow>
|
|
<mi>Γ</mi>
|
|
<mfenced>
|
|
<mrow>
|
|
<mi>a</mi>
|
|
</mrow>
|
|
</mfenced>
|
|
</mrow>
|
|
</mfrac>
|
|
<mspace width="1em"/>
|
|
<mo>=</mo>
|
|
<mspace width="1em"/>
|
|
<msup>
|
|
<mi>e</mi>
|
|
<mrow>
|
|
<mi>x</mi>
|
|
<mo>−</mo>
|
|
<mi>a</mi>
|
|
</mrow>
|
|
</msup>
|
|
<msup>
|
|
<mfenced>
|
|
<mrow>
|
|
<mfrac>
|
|
<mi>x</mi>
|
|
<mrow>
|
|
<mi>a</mi>
|
|
<mo>+</mo>
|
|
<mi>g</mi>
|
|
<mo>−</mo>
|
|
<mn>0.5</mn>
|
|
</mrow>
|
|
</mfrac>
|
|
</mrow>
|
|
</mfenced>
|
|
<mi>a</mi>
|
|
</msup>
|
|
<msqrt>
|
|
<mrow>
|
|
<mfrac>
|
|
<mrow>
|
|
<mi>a</mi>
|
|
<mo>+</mo>
|
|
<mi>g</mi>
|
|
<mo>−</mo>
|
|
<mn>0.5</mn>
|
|
</mrow>
|
|
<mi>e</mi>
|
|
</mfrac>
|
|
</mrow>
|
|
</msqrt>
|
|
<mfrac>
|
|
<mn>1</mn>
|
|
<mrow>
|
|
<mi>L</mi>
|
|
<mfenced>
|
|
<mrow>
|
|
<mi>a</mi>
|
|
</mrow>
|
|
</mfenced>
|
|
</mrow>
|
|
</mfrac>
|
|
</mrow>
|
|
</math>
|
|
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
|
|
<mrow>
|
|
<msup>
|
|
<mi>e</mi>
|
|
<mrow>
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|
<mi>x</mi>
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|
<mo>−</mo>
|
|
<mi>a</mi>
|
|
</mrow>
|
|
</msup>
|
|
<msup>
|
|
<mfenced>
|
|
<mrow>
|
|
<mfrac>
|
|
<mi>x</mi>
|
|
<mrow>
|
|
<mi>a</mi>
|
|
<mo>+</mo>
|
|
<mi>g</mi>
|
|
<mo>−</mo>
|
|
<mn>0.5</mn>
|
|
</mrow>
|
|
</mfrac>
|
|
</mrow>
|
|
</mfenced>
|
|
<mi>a</mi>
|
|
</msup>
|
|
<mspace width="1em"/>
|
|
<mo>=</mo>
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|
<mspace width="1em"/>
|
|
<msup>
|
|
<mi>e</mi>
|
|
<mfenced>
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|
<mrow>
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|
<mi>a</mi>
|
|
<mtext>log1pmx</mtext>
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<mfenced>
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<mrow>
|
|
<mfrac>
|
|
<mrow>
|
|
<mi>x</mi>
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|
<mo>−</mo>
|
|
<mi>a</mi>
|
|
<mo>−</mo>
|
|
<mi>g</mi>
|
|
<mo>+</mo>
|
|
<mn>0.5</mn>
|
|
</mrow>
|
|
<mrow>
|
|
<mi>a</mi>
|
|
<mo>+</mo>
|
|
<mi>g</mi>
|
|
<mo>−</mo>
|
|
<mn>0.5</mn>
|
|
</mrow>
|
|
</mfrac>
|
|
</mrow>
|
|
</mfenced>
|
|
<mo>+</mo>
|
|
<mfrac>
|
|
<mrow>
|
|
<mi>x</mi>
|
|
<mfenced>
|
|
<mrow>
|
|
<mn>0.5</mn>
|
|
<mo>−</mo>
|
|
<mi>g</mi>
|
|
</mrow>
|
|
</mfenced>
|
|
</mrow>
|
|
<mrow>
|
|
<mi>a</mi>
|
|
<mo>+</mo>
|
|
<mi>g</mi>
|
|
<mo>−</mo>
|
|
<mn>0.5</mn>
|
|
</mrow>
|
|
</mfrac>
|
|
</mrow>
|
|
</mfenced>
|
|
</msup>
|
|
<mspace width="1em"/>
|
|
<mo>;</mo>
|
|
<mspace width="1em"/>
|
|
<mtext>log1pmx</mtext>
|
|
<mfenced>
|
|
<mrow>
|
|
<mi>z</mi>
|
|
</mrow>
|
|
</mfenced>
|
|
<mo>=</mo>
|
|
<mi>ln</mi>
|
|
<mfenced>
|
|
<mrow>
|
|
<mn>1</mn>
|
|
<mo>+</mo>
|
|
<mi>z</mi>
|
|
</mrow>
|
|
</mfenced>
|
|
<mo>−</mo>
|
|
<mi>z</mi>
|
|
</mrow>
|
|
</math>
|
|
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
|
|
<mrow>
|
|
<mtext>gp1m1</mtext>
|
|
<mfenced>
|
|
<mrow>
|
|
<mi>z</mi>
|
|
</mrow>
|
|
</mfenced>
|
|
<mspace width="1em"/>
|
|
<mo>=</mo>
|
|
<mspace width="1em"/>
|
|
<msqrt>
|
|
<mrow>
|
|
<mn>1</mn>
|
|
<mo>+</mo>
|
|
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|
|
<mfrac>
|
|
<mi>z</mi>
|
|
<mrow>
|
|
<mi>g</mi>
|
|
<mo>+</mo>
|
|
<mn>0.5</mn>
|
|
</mrow>
|
|
</mfrac>
|
|
</mrow>
|
|
</mrow>
|
|
</msqrt>
|
|
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|
|
<mrow>
|
|
<mo>[</mo>
|
|
<msup>
|
|
<mfenced>
|
|
<mrow>
|
|
<mfrac>
|
|
<mrow>
|
|
<mi>z</mi>
|
|
<mo>+</mo>
|
|
<mi>g</mi>
|
|
<mo>−</mo>
|
|
<mn>0.5</mn>
|
|
</mrow>
|
|
<mi>e</mi>
|
|
</mfrac>
|
|
</mrow>
|
|
</mfenced>
|
|
<mi>z</mi>
|
|
</msup>
|
|
<mo>−</mo>
|
|
<mn>1</mn>
|
|
<mo>]</mo>
|
|
<mo>+</mo>
|
|
<mo>[</mo>
|
|
<mi>L</mi>
|
|
<mfenced>
|
|
<mrow>
|
|
<mi>z</mi>
|
|
</mrow>
|
|
</mfenced>
|
|
<mo>−</mo>
|
|
<mn>1</mn>
|
|
<mo>]</mo>
|
|
<msup>
|
|
<mfenced>
|
|
<mrow>
|
|
<mfrac>
|
|
<mrow>
|
|
<mi>z</mi>
|
|
<mo>+</mo>
|
|
<mi>g</mi>
|
|
<mo>−</mo>
|
|
<mn>0.5</mn>
|
|
</mrow>
|
|
<mi>e</mi>
|
|
</mfrac>
|
|
</mrow>
|
|
</mfenced>
|
|
<mi>z</mi>
|
|
</msup>
|
|
</mrow>
|
|
</mfenced>
|
|
<mo>+</mo>
|
|
<mo>[</mo>
|
|
<msqrt>
|
|
<mrow>
|
|
<mn>1</mn>
|
|
<mo>+</mo>
|
|
<mrow>
|
|
<mfrac>
|
|
<mi>z</mi>
|
|
<mrow>
|
|
<mi>g</mi>
|
|
<mo>+</mo>
|
|
<mn>0.5</mn>
|
|
</mrow>
|
|
</mfrac>
|
|
</mrow>
|
|
</mrow>
|
|
</msqrt>
|
|
<mo>−</mo>
|
|
<mn>1</mn>
|
|
<mo>]</mo>
|
|
</mrow>
|
|
</math>
|
|
</body>
|
|
</html> |