41 lines
1.3 KiB
Markdown
41 lines
1.3 KiB
Markdown
[sf.cmath.legendre]
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# 29 Numerics library [[numerics]](./#numerics)
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## 29.7 Mathematical functions for floating-point types [[c.math]](c.math#sf.cmath.legendre)
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### 29.7.6 Mathematical special functions [[sf.cmath]](sf.cmath#legendre)
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#### 29.7.6.18 Legendre polynomials [sf.cmath.legendre]
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[ð](#lib:legendre)
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`floating-point-type legendre(unsigned l, floating-point-type x);
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float legendref(unsigned l, float x);
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long double legendrel(unsigned l, long double x);
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`
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[1](#1)
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[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L10632)
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*Effects*: These functions compute the Legendre polynomials of their
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respective argumentsl and x[.](#1.sentence-1)
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[2](#2)
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[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L10638)
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*Returns*: Pâ(x),
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where Pâ is given by Formula [29.38](#eq:sf.cmath.legendre),l is l, andx is x[.](#2.sentence-1)
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Pâ(x)=12ââ!dâdxâ(x2â1)â , for |x|â¤1(29.38)
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[3](#3)
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[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L10651)
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*Remarks*: The effect of calling each of these functions
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is implementation-defined
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if l >= 128[.](#3.sentence-1)
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