1<?xml version="1.0" encoding="UTF-8"?> 2<!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'>]> 3<html xmlns="http://www.w3.org/1999/xhtml"> 4<head><title>legendre_2</title> 5<!-- MathML created with MathCast Equation Editor version 0.92 --> 6</head> 7<body> 8<math xmlns="http://www.w3.org/1998/Math/MathML" display="block"> 9 <mrow> 10 <mtable columnalign="right center center center left"> 11 <mtr> 12 <mtd> 13 <mtext>legendre_q</mtext> 14 <mfenced> 15 <mrow> 16 <mn>0,</mn> 17 <mi>x</mi> 18 </mrow> 19 </mfenced> 20 </mtd> 21 <mtd> 22 <mo>=</mo> 23 </mtd> 24 <mtd> 25 <msub> 26 <mi>Q</mi> 27 <mn>0</mn> 28 </msub> 29 <mfenced> 30 <mrow> 31 <mi>x</mi> 32 </mrow> 33 </mfenced> 34 </mtd> 35 <mtd> 36 <mo>=</mo> 37 </mtd> 38 <mtd> 39 <mfrac> 40 <mn>1</mn> 41 <mn>2</mn> 42 </mfrac> 43 <mi>ln</mi> 44 <mfenced> 45 <mrow> 46 <mfrac> 47 <mrow> 48 <mn>1</mn> 49 <mo>+</mo> 50 <mi>x</mi> 51 </mrow> 52 <mrow> 53 <mn>1</mn> 54 <mo>−</mo> 55 <mi>x</mi> 56 </mrow> 57 </mfrac> 58 </mrow> 59 </mfenced> 60 </mtd> 61 </mtr> 62 <mtr> 63 <mtd> 64 <mtext>legendre_q</mtext> 65 <mfenced> 66 <mrow> 67 <mn>1,</mn> 68 <mi>x</mi> 69 </mrow> 70 </mfenced> 71 </mtd> 72 <mtd> 73 <mo>=</mo> 74 </mtd> 75 <mtd> 76 <msub> 77 <mi>Q</mi> 78 <mn>1</mn> 79 </msub> 80 <mfenced> 81 <mrow> 82 <mi>x</mi> 83 </mrow> 84 </mfenced> 85 </mtd> 86 <mtd> 87 <mo>=</mo> 88 </mtd> 89 <mtd> 90 <mfrac> 91 <mi>x</mi> 92 <mn>2</mn> 93 </mfrac> 94 <mi>ln</mi> 95 <mfenced> 96 <mrow> 97 <mfrac> 98 <mrow> 99 <mn>1</mn> 100 <mo>+</mo> 101 <mi>x</mi> 102 </mrow> 103 <mrow> 104 <mn>1</mn> 105 <mo>−</mo> 106 <mi>x</mi> 107 </mrow> 108 </mfrac> 109 </mrow> 110 </mfenced> 111 <mo>−</mo> 112 <mn>1</mn> 113 </mtd> 114 </mtr> 115 </mtable> 116 </mrow> 117</math></body> 118</html>