1<?xml version='1.0'?> 2<!DOCTYPE html PUBLIC '-//W3C//DTD XHTML 1.1 plus MathML 2.0//EN' 3 'http://www.w3.org/TR/MathML2/dtd/xhtml-math11-f.dtd' 4 [<!ENTITY mathml 'http://www.w3.org/1998/Math/MathML'>]> 5<html xmlns='http://www.w3.org/1999/xhtml'> 6<head><title>hypergeometric1</title> 7<!-- MathML created with MathCast Equation Editor version 0.89 --> 8</head> 9<body> 10<math xmlns="http://www.w3.org/1998/Math/MathML" display="block"> 11 <mrow> 12 <mi>f</mi> 13 <mfenced> 14 <mrow> 15 <mi>k</mi> 16 <mo>;</mo> 17 <mi>r</mi> 18 <mo>,</mo> 19 <mi>n</mi> 20 <mo>,</mo> 21 <mi>N</mi> 22 </mrow> 23 </mfenced> 24 <mspace width="1em"/> 25 <mo>=</mo> 26 <mspace width="1em"/> 27 <mfrac> 28 <mrow> 29 <mi>n</mi> 30 <mo>!</mo> 31 <mi>r</mi> 32 <mo>!</mo> 33 <mfenced> 34 <mrow> 35 <mi>N</mi> 36 <mo>−</mo> 37 <mi>n</mi> 38 </mrow> 39 </mfenced> 40 <mo>!</mo> 41 <mfenced> 42 <mrow> 43 <mi>N</mi> 44 <mo>−</mo> 45 <mi>r</mi> 46 </mrow> 47 </mfenced> 48 <mo>!</mo> 49 </mrow> 50 <mrow> 51 <mi>N</mi> 52 <mo>!</mo> 53 <mi>k</mi> 54 <mo>!</mo> 55 <mfenced> 56 <mrow> 57 <mi>n</mi> 58 <mo>−</mo> 59 <mi>k</mi> 60 </mrow> 61 </mfenced> 62 <mo>!</mo> 63 <mfenced> 64 <mrow> 65 <mi>r</mi> 66 <mo>−</mo> 67 <mi>k</mi> 68 </mrow> 69 </mfenced> 70 <mo>!</mo> 71 <mfenced> 72 <mrow> 73 <mi>N</mi> 74 <mo>−</mo> 75 <mi>n</mi> 76 <mo>−</mo> 77 <mi>r</mi> 78 <mo>+</mo> 79 <mi>k</mi> 80 </mrow> 81 </mfenced> 82 <mo>!</mo> 83 </mrow> 84 </mfrac> 85 <mspace width="1em"/> 86 <mo>;</mo> 87 <mspace width="1em"/> 88 <mi>max</mi> 89 <mfenced> 90 <mrow> 91 <mn>0,</mn> 92 <mi>N</mi> 93 <mo>−</mo> 94 <mi>r</mi> 95 <mo>−</mo> 96 <mi>n</mi> 97 <mo>+</mo> 98 <mi>k</mi> 99 </mrow> 100 </mfenced> 101 <mo><</mo> 102 <mo>=</mo> 103 <mi>k</mi> 104 <mo><</mo> 105 <mo>=</mo> 106 <mi>min</mi> 107 <mfenced> 108 <mrow> 109 <mi>r</mi> 110 <mo>,</mo> 111 <mi>n</mi> 112 </mrow> 113 </mfenced> 114 </mrow> 115</math> 116</body> 117</html> 118