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.
Notes
Note that this implementation includes the Condon-Shortley phase.
Array API Standard Support
lpmv
has experimental support for Python Array API Standard compatible backends in addition to NumPy. Please consider testing these features by setting an environment variableSCIPY_ARRAY_API=1
and providing CuPy, PyTorch, JAX, or Dask arrays as array arguments. The following combinations of backend and device (or other capability) are supported.Library
CPU
GPU
NumPy
✅
n/a
CuPy
n/a
✅
PyTorch
✅
⛔
JAX
⚠️ no JIT
⛔
Dask
✅
n/a
See Support for the array API standard for more information.
References
[1]Zhang, Jin, “Computation of Special Functions”, John Wiley and Sons, Inc, 1996.