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nest-open-source / nest-learning-thermostat / 5.0 / boost / 317601cb979f96545d0e892ce7cfdf59f676ee0a / . / boost_1_45_0 / libs / math / doc / sf_and_dist / equations / spherical_3.mml
blob: afa61c5eb40e06b5a949f92e4c37974dbaa722ed [file] [log] [blame]
<?xml version='1.0'?>
<!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'>]>
<html xmlns='http://www.w3.org/1999/xhtml'>
<head><title>spherical_3</title>
<!-- MathML created with MathCast Equation Editor version 0.88 -->
</head>
<body>
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mrow>
<mtext>sph_legendre</mtext>
<mfenced>
<mrow>
<mi>l</mi>
<mo>,</mo>
<mi>m</mi>
<mo>,</mo>
<mi>&#x03B8;</mi>
</mrow>
</mfenced>
<mspace width="1em"/>
<mo>=</mo>
<mspace width="1em"/>
<msubsup>
<mi>Y</mi>
<mrow>
<mi>l</mi>
</mrow>
<mi>m</mi>
</msubsup>
<mfenced>
<mrow>
<mi>&#x03B8;</mi>
<mo>,</mo>
<mn>0</mn>
</mrow>
</mfenced>
<mspace width="1em"/>
<mo>=</mo>
<mspace width="1em"/>
<msup>
<mfenced>
<mrow>
<mo>&#x2212;</mo>
<mn>1</mn>
</mrow>
</mfenced>
<mi>m</mi>
</msup>
<msqrt>
<mrow>
<mfrac>
<mrow>
<mn>2</mn>
<mi>l</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
<mrow>
<mn>4</mn>
<mi>&#x03C0;</mi>
</mrow>
</mfrac>
<mfrac>
<mrow>
<mfenced>
<mrow>
<mi>l</mi>
<mo>&#x2212;</mo>
<mi>m</mi>
</mrow>
</mfenced>
<mo>!</mo>
</mrow>
<mrow>
<mfenced>
<mrow>
<mi>l</mi>
<mo>+</mo>
<mi>m</mi>
</mrow>
</mfenced>
<mo>!</mo>
</mrow>
</mfrac>
</mrow>
</msqrt>
<msubsup>
<mi>P</mi>
<mrow>
<mi>l</mi>
</mrow>
<mi>m</mi>
</msubsup>
<mfenced>
<mrow>
<mi>cos</mi>
<mi>&#x03B8;</mi>
</mrow>
</mfenced>
</mrow>
</math>
</body>
</html>