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_3</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 left"> 11 <mtr> 12 <mtd> 13 <msubsup> 14 <mi>P</mi> 15 <mrow> 16 <mi>l</mi> 17 </mrow> 18 <mrow> 19 <mo>−</mo> 20 <mi>m</mi> 21 </mrow> 22 </msubsup> 23 <mfenced> 24 <mrow> 25 <mi>x</mi> 26 </mrow> 27 </mfenced> 28 </mtd> 29 <mtd> 30 <mo>=</mo> 31 </mtd> 32 <mtd> 33 <msup> 34 <mfenced> 35 <mrow> 36 <mo>−</mo> 37 <mn>1</mn> 38 </mrow> 39 </mfenced> 40 <mi>m</mi> 41 </msup> 42 <mfrac> 43 <mrow> 44 <mfenced> 45 <mrow> 46 <mi>l</mi> 47 <mo>−</mo> 48 <mi>m</mi> 49 </mrow> 50 </mfenced> 51 <mo>!</mo> 52 </mrow> 53 <mrow> 54 <mfenced> 55 <mrow> 56 <mi>l</mi> 57 <mo>+</mo> 58 <mi>m</mi> 59 </mrow> 60 </mfenced> 61 <mo>!</mo> 62 </mrow> 63 </mfrac> 64 <msubsup> 65 <mi>P</mi> 66 <mrow> 67 <mi>l</mi> 68 </mrow> 69 <mi>m</mi> 70 </msubsup> 71 <mfenced> 72 <mrow> 73 <mi>x</mi> 74 </mrow> 75 </mfenced> 76 </mtd> 77 </mtr> 78 <mtr> 79 <mtd> 80 <msubsup> 81 <mi>P</mi> 82 <mrow> 83 <mo>−</mo> 84 <mi>l</mi> 85 <mo>−</mo> 86 <mn>1</mn> 87 </mrow> 88 <mi>m</mi> 89 </msubsup> 90 <mfenced> 91 <mrow> 92 <mi>x</mi> 93 </mrow> 94 </mfenced> 95 </mtd> 96 <mtd> 97 <mo>=</mo> 98 </mtd> 99 <mtd> 100 <msubsup> 101 <mi>P</mi> 102 <mrow> 103 <mi>l</mi> 104 </mrow> 105 <mi>m</mi> 106 </msubsup> 107 <mfenced> 108 <mrow> 109 <mi>x</mi> 110 </mrow> 111 </mfenced> 112 </mtd> 113 </mtr> 114 </mtable> 115 </mrow> 116</math></body> 117</html>