mirror of
https://github.com/boostorg/math.git
synced 2026-01-31 08:22:09 +00:00
373e1d49b9
Also made sure that all the files are readable by the latest Mathcast release, and by SVGMath, and are valid XML. [SVN r39535]
497 lines
9.6 KiB
XML
497 lines
9.6 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>beta</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>b</mi>
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</mrow>
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</mfenced>
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<mo>=</mo>
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<mi>B</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>b</mi>
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</mrow>
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</mfenced>
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<mo>=</mo>
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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>
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<mi>Γ</mi>
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<mfenced>
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<mrow>
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<mi>b</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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<mo>+</mo>
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<mi>b</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>beta</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>b</mi>
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</mrow>
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</mfenced>
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<mo>=</mo>
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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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<mi>a</mi>
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<mo>+</mo>
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<mi>g</mi>
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<mo>−</mo>
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<mn>0.5</mn>
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</mrow>
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<mrow>
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<mi>a</mi>
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<mo>+</mo>
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<mi>b</mi>
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<mo>+</mo>
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<mi>g</mi>
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<mo>−</mo>
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<mn>0.5</mn>
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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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<mi>a</mi>
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<mo>−</mo>
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<mn>0.5</mn>
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</mrow>
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</msup>
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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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<mi>b</mi>
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<mo>+</mo>
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<mi>g</mi>
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<mo>−</mo>
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<mn>0.5</mn>
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</mrow>
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<mrow>
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<mi>a</mi>
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<mo>+</mo>
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<mi>b</mi>
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<mo>+</mo>
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<mi>g</mi>
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<mo>−</mo>
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<mn>0.5</mn>
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</mrow>
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</mfrac>
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</mrow>
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</mfenced>
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<mi>b</mi>
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</msup>
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<msqrt>
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<mrow>
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<mfrac>
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<mi>e</mi>
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<mrow>
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<mi>b</mi>
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<mo>+</mo>
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<mi>g</mi>
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<mo>−</mo>
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<mn>0.5</mn>
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</mrow>
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</mfrac>
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</mrow>
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</msqrt>
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<mfrac>
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<mrow>
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<mi>L</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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<mi>L</mi>
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<mfenced>
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<mrow>
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<mi>b</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>L</mi>
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<mfenced>
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<mrow>
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<mi>c</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>beta</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>b</mi>
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</mrow>
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</mfenced>
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<mo>=</mo>
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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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<mi>a</mi>
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<mo>+</mo>
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<mi>g</mi>
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<mo>−</mo>
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<mn>0.5</mn>
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</mrow>
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<mrow>
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<mi>a</mi>
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<mo>+</mo>
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<mi>b</mi>
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<mo>+</mo>
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<mi>g</mi>
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<mo>−</mo>
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<mn>0.5</mn>
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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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<mi>a</mi>
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<mo>−</mo>
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<mi>b</mi>
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<mo>−</mo>
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<mn>0.5</mn>
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</mrow>
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</msup>
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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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<mfenced>
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<mrow>
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<mi>a</mi>
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<mo>+</mo>
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<mi>g</mi>
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<mo>−</mo>
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<mn>0.5</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>b</mi>
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<mo>+</mo>
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<mi>g</mi>
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<mo>−</mo>
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<mn>0.5</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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<msup>
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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>b</mi>
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<mo>+</mo>
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<mi>g</mi>
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<mo>−</mo>
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<mn>0.5</mn>
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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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</mfrac>
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</mrow>
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</mfenced>
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<mi>b</mi>
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</msup>
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<msqrt>
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<mrow>
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<mfrac>
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<mi>e</mi>
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<mrow>
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<mi>b</mi>
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<mo>+</mo>
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<mi>g</mi>
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<mo>−</mo>
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<mn>0.5</mn>
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</mrow>
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</mfrac>
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</mrow>
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</msqrt>
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<mfrac>
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<mrow>
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<mi>L</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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<mi>L</mi>
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<mfenced>
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<mrow>
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<mi>b</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>L</mi>
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<mfenced>
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<mrow>
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<mi>c</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>beta</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>b</mi>
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</mrow>
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</mfenced>
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<mo>=</mo>
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<mfrac>
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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>b</mi>
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</mrow>
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</mfenced>
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<mi>b</mi>
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</mfrac>
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<mtext>beta</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>b</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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</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>beta</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>b</mi>
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</mrow>
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</mfenced>
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<mo>=</mo>
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<mfrac>
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<mrow>
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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>b</mi>
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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>a</mi>
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<mo>+</mo>
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<mi>b</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>a</mi>
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<mi>b</mi>
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</mrow>
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</mfrac>
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<mtext>beta</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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<mn>1,</mn>
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<mi>b</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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</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>i</mi>
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<mi>f</mi>
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<mspace width="1em"/>
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<mi>a</mi>
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<mo>≫</mo>
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<mi>b</mi>
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<mspace width="1em"/>
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<mi>a</mi>
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<mi>n</mi>
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<mi>d</mi>
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<mspace width="1em"/>
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<mi>a</mi>
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<mo>+</mo>
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<mi>b</mi>
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<mo>=</mo>
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<mi>a</mi>
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<mspace width="1em"/>
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<mspace width="1em"/>
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<mi>t</mi>
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<mi>h</mi>
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<mi>e</mi>
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<mi>n</mi>
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<mo>:</mo>
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<mspace width="1em"/>
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<mspace width="1em"/>
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<mi>b</mi>
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<mi>e</mi>
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<mi>t</mi>
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<mi>a</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>b</mi>
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</mrow>
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</mfenced>
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<mo>=</mo>
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<mi>Γ</mi>
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<mfenced>
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<mrow>
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<mi>b</mi>
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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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<mtext>if</mtext>
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<mspace width="1em"/>
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<mi>a</mi>
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<mo>=</mo>
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<mn>1</mn>
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<mspace width="1em"/>
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<mspace width="1em"/>
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<mtext>then:</mtext>
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<mspace width="1em"/>
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<mspace width="1em"/>
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<mtext>beta</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>b</mi>
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</mrow>
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</mfenced>
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<mo>=</mo>
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<mfrac>
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<mn>1</mn>
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<mi>b</mi>
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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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<msup>
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<mi>e</mi>
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<mrow>
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<mi>l</mi>
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<mi>c</mi>
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<mo>−</mo>
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<mi>l</mi>
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<mi>a</mi>
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<mo>−</mo>
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<mi>l</mi>
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<mi>b</mi>
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</mrow>
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</msup>
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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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<mi>l</mi>
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<mi>a</mi>
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</mrow>
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<mrow>
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<mi>l</mi>
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<mi>c</mi>
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</mrow>
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</mfrac>
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</mrow>
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</mfenced>
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<mi>a</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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<mfrac>
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<mrow>
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<mi>l</mi>
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<mi>b</mi>
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</mrow>
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<mrow>
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<mi>l</mi>
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<mi>c</mi>
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</mrow>
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</mfrac>
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</mrow>
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</mfenced>
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<mi>b</mi>
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</msup>
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</mrow>
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</math>
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</body>
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</html> |