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>spherical_3</title> 7<!-- MathML created with MathCast Equation Editor version 0.88 --> 8</head> 9<body> 10<math xmlns="http://www.w3.org/1998/Math/MathML" display="block"> 11 <mrow> 12 <mtext>sph_legendre</mtext> 13 <mfenced> 14 <mrow> 15 <mi>l</mi> 16 <mo>,</mo> 17 <mi>m</mi> 18 <mo>,</mo> 19 <mi>θ</mi> 20 </mrow> 21 </mfenced> 22 <mspace width="1em"/> 23 <mo>=</mo> 24 <mspace width="1em"/> 25 <msubsup> 26 <mi>Y</mi> 27 <mrow> 28 <mi>l</mi> 29 </mrow> 30 <mi>m</mi> 31 </msubsup> 32 <mfenced> 33 <mrow> 34 <mi>θ</mi> 35 <mo>,</mo> 36 <mn>0</mn> 37 </mrow> 38 </mfenced> 39 <mspace width="1em"/> 40 <mo>=</mo> 41 <mspace width="1em"/> 42 <msup> 43 <mfenced> 44 <mrow> 45 <mo>−</mo> 46 <mn>1</mn> 47 </mrow> 48 </mfenced> 49 <mi>m</mi> 50 </msup> 51 <msqrt> 52 <mrow> 53 <mfrac> 54 <mrow> 55 <mn>2</mn> 56 <mi>l</mi> 57 <mo>+</mo> 58 <mn>1</mn> 59 </mrow> 60 <mrow> 61 <mn>4</mn> 62 <mi>π</mi> 63 </mrow> 64 </mfrac> 65 <mfrac> 66 <mrow> 67 <mfenced> 68 <mrow> 69 <mi>l</mi> 70 <mo>−</mo> 71 <mi>m</mi> 72 </mrow> 73 </mfenced> 74 <mo>!</mo> 75 </mrow> 76 <mrow> 77 <mfenced> 78 <mrow> 79 <mi>l</mi> 80 <mo>+</mo> 81 <mi>m</mi> 82 </mrow> 83 </mfenced> 84 <mo>!</mo> 85 </mrow> 86 </mfrac> 87 </mrow> 88 </msqrt> 89 <msubsup> 90 <mi>P</mi> 91 <mrow> 92 <mi>l</mi> 93 </mrow> 94 <mi>m</mi> 95 </msubsup> 96 <mfenced> 97 <mrow> 98 <mi>cos</mi> 99 <mi>θ</mi> 100 </mrow> 101 </mfenced> 102 </mrow> 103</math> 104</body> 105</html> 106