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>polygamma4</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 <mi>n</mi> 44 <mo>!</mo> 45 </mrow> 46 <msup> 47 <mi>x</mi> 48 <mrow> 49 <mi>n</mi> 50 <mo>+</mo> 51 <mn>1</mn> 52 </mrow> 53 </msup> 54 </mfrac> 55 <mo>+</mo> 56 <munderover> 57 <mo>∑</mo> 58 <mrow> 59 <mi>k</mi> 60 <mo>=</mo> 61 <mn>0</mn> 62 </mrow> 63 <mi>∞</mi> 64 </munderover> 65 <mfrac> 66 <mrow> 67 <msup> 68 <mfenced> 69 <mrow> 70 <mo>−</mo> 71 <mn>1</mn> 72 </mrow> 73 </mfenced> 74 <mrow> 75 <mi>k</mi> 76 <mo>+</mo> 77 <mi>n</mi> 78 <mo>+</mo> 79 <mn>1</mn> 80 </mrow> 81 </msup> 82 <mfenced> 83 <mrow> 84 <mi>k</mi> 85 <mo>+</mo> 86 <mi>n</mi> 87 </mrow> 88 </mfenced> 89 <mo>!</mo> 90 <mi>ζ</mi> 91 <mfenced> 92 <mrow> 93 <mi>k</mi> 94 <mo>+</mo> 95 <mi>n</mi> 96 <mo>+</mo> 97 <mn>1</mn> 98 </mrow> 99 </mfenced> 100 <msup> 101 <mi>x</mi> 102 <mi>k</mi> 103 </msup> 104 </mrow> 105 <mrow> 106 <mi>k</mi> 107 <mo>!</mo> 108 </mrow> 109 </mfrac> 110 </mrow> 111</math> 112</body> 113</html>