scipy.special.lpmv#
- scipy.special.lpmv(m, v, x, out=None) = <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:
- marray_like
- Order (int or float). If passed a float not equal to an integer the function returns NaN. 
- varray_like
- Degree (float). 
- xarray_like
- Argument (float). Must have - |x| <= 1.
- outndarray, optional
- Optional output array for the function results 
 
- Returns:
- pmvscalar or ndarray
- Value of the associated Legendre function. 
 
 - See also - Notes - Note that this implementation includes the Condon-Shortley phase. - References [1]- Zhang, Jin, “Computation of Special Functions”, John Wiley and Sons, Inc, 1996.