303 lines
7.7 KiB
XML
303 lines
7.7 KiB
XML
<?xml version="1.0" encoding="UTF-8"?>
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<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.1 plus MathML 2.0//EN" "http://www.w3.org/TR/MathML2/dtd/xhtml-math11-f.dtd" [<!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><title>hypergeometric6</title>
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<!-- MathML created with MathCast Equation Editor version 0.89 -->
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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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<mtable columnalign="right center left">
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<mtr>
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<mtd>
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<mtext>mean</mtext>
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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>r</mi>
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<mi>n</mi>
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</mrow>
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<mi>N</mi>
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</mfrac>
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</mtd>
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</mtr>
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<mtr>
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<mtd>
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<mtext>mode</mtext>
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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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<mtext>floor</mtext>
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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>r</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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<mrow>
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<mi>N</mi>
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<mo>+</mo>
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<mn>2</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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</mtd>
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</mtr>
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<mtr>
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<mtd>
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<mtext>variance</mtext>
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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>r</mi>
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<mfenced>
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<mrow>
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<mfrac>
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<mi>n</mi>
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<mi>N</mi>
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</mfrac>
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</mrow>
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</mfenced>
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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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<mfrac>
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<mi>n</mi>
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<mi>N</mi>
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</mfrac>
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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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<mi>r</mi>
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</mrow>
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</mfenced>
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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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<mn>1</mn>
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</mrow>
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</mfenced>
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</mfrac>
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</mtd>
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</mtr>
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<mtr>
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<mtd>
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<mtext>skewness</mtext>
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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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<mfenced>
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<mrow>
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<mi>N</mi>
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<mo>−</mo>
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<mn>2</mn>
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<mi>n</mi>
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</mrow>
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</mfenced>
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<msqrt>
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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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</msqrt>
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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>2</mn>
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<mi>r</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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<msqrt>
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<mrow>
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<mi>r</mi>
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<mi>n</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>n</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>N</mi>
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<mo>−</mo>
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<mi>r</mi>
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</mrow>
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</mfenced>
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</mrow>
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</msqrt>
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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>2</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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<mtr>
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<mtd>
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<mtext>kurtosis excess</mtext>
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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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<mfenced>
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<mrow>
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<mfrac>
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<mrow>
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<msup>
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<mi>N</mi>
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<mn>2</mn>
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</msup>
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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>r</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>2</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>3</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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<mi>r</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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</mfenced>
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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>N</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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<mo>−</mo>
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<mn>6</mn>
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<mi>N</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>r</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>n</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>n</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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<mo>+</mo>
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<mfrac>
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<mrow>
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<mn>3</mn>
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<mi>r</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>r</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>N</mi>
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<mo>+</mo>
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<mn>6</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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<mi>N</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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<mo>−</mo>
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<mn>6</mn>
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</mrow>
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</mfenced>
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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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</body>
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</html> |