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>polygamma5</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 <msup> 13 <mi>ψ</mi> 14 <mrow> 15 <mfenced> 16 <mrow> 17 <mi>n</mi> 18 </mrow> 19 </mfenced> 20 </mrow> 21 </msup> 22 <mfenced> 23 <mrow> 24 <mi>x</mi> 25 </mrow> 26 </mfenced> 27 <mo>∝</mo> 28 <mfrac> 29 <mrow> 30 <msup> 31 <mfenced> 32 <mrow> 33 <mo>−</mo> 34 <mn>1</mn> 35 </mrow> 36 </mfenced> 37 <mrow> 38 <mi>n</mi> 39 <mo>−</mo> 40 <mn>1</mn> 41 </mrow> 42 </msup> 43 <mfenced> 44 <mrow> 45 <mi>n</mi> 46 <mo>−</mo> 47 <mn>1</mn> 48 </mrow> 49 </mfenced> 50 <mo>!</mo> 51 <mfenced> 52 <mrow> 53 <mi>n</mi> 54 <mo>+</mo> 55 <mn>2</mn> 56 <mi>x</mi> 57 </mrow> 58 </mfenced> 59 </mrow> 60 <mrow> 61 <mn>2</mn> 62 <msup> 63 <mi>x</mi> 64 <mrow> 65 <mi>n</mi> 66 <mo>+</mo> 67 <mn>1</mn> 68 </mrow> 69 </msup> 70 </mrow> 71 </mfrac> 72 <mo>−</mo> 73 <msup> 74 <mfenced> 75 <mrow> 76 <mo>−</mo> 77 <mn>1</mn> 78 </mrow> 79 </mfenced> 80 <mi>n</mi> 81 </msup> 82 <munderover> 83 <mo>∑</mo> 84 <mrow> 85 <mi>k</mi> 86 <mo>=</mo> 87 <mn>1</mn> 88 </mrow> 89 <mi>∞</mi> 90 </munderover> 91 <mfrac> 92 <mrow> 93 <mfenced> 94 <mrow> 95 <mn>2</mn> 96 <mi>k</mi> 97 <mo>+</mo> 98 <mi>n</mi> 99 <mo>−</mo> 100 <mn>1</mn> 101 </mrow> 102 </mfenced> 103 <mo>!</mo> 104 </mrow> 105 <mrow> 106 <mfenced> 107 <mrow> 108 <mn>2</mn> 109 <mi>k</mi> 110 </mrow> 111 </mfenced> 112 <mo>!</mo> 113 <msup> 114 <mi>x</mi> 115 <mrow> 116 <mn>2</mn> 117 <mi>k</mi> 118 <mo>+</mo> 119 <mi>n</mi> 120 </mrow> 121 </msup> 122 </mrow> 123 </mfrac> 124 <msub> 125 <mi>B</mi> 126 <mrow> 127 <mn>2</mn> 128 <mi>k</mi> 129 </mrow> 130 </msub> 131 </mrow> 132</math> 133</body> 134</html>