bundles / scipy 1.17.1 / scipy / special / _multiufuncs / sph_legendre_p

MultiUFunc

`scipy.special._multiufuncs:sph_legendre_p`

source: /scipy/special/_multiufuncs.py

Signature

def sph_legendre_p ( n , m , theta , * , diff_n = 0 )

Summary

Spherical Legendre polynomial of the first kind.

Parameters

n : ArrayLike[int]: Degree of the spherical Legendre polynomial. Must have n >= 0.
m : ArrayLike[int]: Order of the spherical Legendre polynomial.
theta : ArrayLike[float]: Input value.
diff_n : Optional[int]: A non-negative integer. Compute and return all derivatives up to order diff_n. Default is 0.

Returns

p : ndarray or tuple[ndarray]: Spherical Legendre polynomial with diff_n derivatives.

Notes

The spherical counterpart of an (unnormalized) associated Legendre polynomial has the additional factor

\frac{( 2 n + 1 ) ( n - m )!}{4 π ( n + m )!}

It is the same as the spherical harmonic $Y_{n}^{m} (θ, ϕ)$ with $ϕ = 0$ .

Aliases

scipy.special.sph_legendre_p

Referenced by

This package

release:1.15.0-notes