tmp/tmpb0g3gr22/{from.md → to.md}
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#### Spherical associated Legendre functions <a id="sf.cmath.sph_legendre">[[sf.cmath.sph_legendre]]</a>
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``` cpp
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double sph_legendre(unsigned l, unsigned m, double theta);
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float sph_legendref(unsigned l, unsigned m, float theta);
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long double sph_legendrel(unsigned l, unsigned m, long double theta);
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```
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*Effects:* These functions compute the spherical associated Legendre
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functions of their respective arguments `l`, `m`, and `theta` (`theta`
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measured in radians).
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*Returns:* $$%
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\mathsf{Y}_\ell^m(\theta, 0)
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\;$$ where $$%
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\mathsf{Y}_\ell^m(\theta, \phi) =
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(-1)^m \left[ \frac{(2 \ell + 1)}
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{4 \pi}
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\frac{(\ell - m)!}
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{(\ell + m)!}
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\right]^{1/2}
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\mathsf{P}_\ell^m
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( \cos\theta ) e ^ {i m \phi},
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\quad \mbox{for $|m| \le \ell$}$$ and l is `l`, m is `m`, and θ
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is `theta`.
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*Remarks:* The effect of calling each of these functions is
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*implementation-defined* if `l >= 128`.
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See also [[sf.cmath.assoc_legendre]].
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