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lpmn(m, n, z)

Computes the associated Legendre function of the first kind of order m and degree n, Pmn(z) = $P_n^m(z)$ , and its derivative, Pmn'(z) . Returns two arrays of size (m+1, n+1) containing Pmn(z) and Pmn'(z) for all orders from 0..m and degrees from 0..n .

This function takes a real argument z . For complex arguments z use clpmn instead.

Notes

In the interval (-1, 1), Ferrer's function of the first kind is returned. The phase convention used for the intervals (1, inf) and (-inf, -1) is such that the result is always real.

Parameters

m : int

|m| <= n ; the order of the Legendre function.

n : int

where n >= 0 ; the degree of the Legendre function. Often called l (lower case L) in descriptions of the associated Legendre function

z : float

Input value.

Returns

Pmn_z : (m+1, n+1) array

Values for all orders 0..m and degrees 0..n

Pmn_d_z : (m+1, n+1) array

Derivatives for all orders 0..m and degrees 0..n

Sequence of associated Legendre functions of the first kind.

See Also

clpmn

associated Legendre functions of the first kind for complex z

Examples

See :

Back References

The following pages refer to to this document either explicitly or contain code examples using this.

scipy.special._basic.clpmn

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GitHub : /scipy/special/_basic.py#1242
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