# scipy.special.lpmv¶

scipy.special.lpmv(m, v, x) = <ufunc 'lpmv'>

Associated Legendre function of integer order and real degree.

Defined as

$P_v^m = (-1)^m (1 - x^2)^{m/2} \frac{d^m}{dx^m} P_v(x)$

where

$P_v = \sum_{k = 0}^\infty \frac{(-v)_k (v + 1)_k}{(k!)^2} \left(\frac{1 - x}{2}\right)^k$

is the Legendre function of the first kind. Here $$(\cdot)_k$$ is the Pochhammer symbol; see poch.

Parameters: m : array_like Order (int or float). If passed a float not equal to an integer the function returns NaN. v : array_like Degree (float). x : array_like Argument (float). Must have |x| <= 1. pmv : ndarray Value of the associated Legendre function.

See also

lpmn
Compute the associated Legendre function for all orders 0, ..., m and degrees 0, ..., n.
clpmn
Compute the associated Legendre function at complex arguments.

Notes

Note that this implementation includes the Condon-Shortley phase.

References

 [R486] Zhang, Jin, “Computation of Special Functions”, John Wiley and Sons, Inc, 1996.

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