scipy.special.poch#
- scipy.special.poch(z, m, out=None) = <ufunc 'poch'>#
Pochhammer symbol.
The Pochhammer symbol (rising factorial) is defined as
\[(z)_m = \frac{\Gamma(z + m)}{\Gamma(z)}\]For positive integer m it reads
\[(z)_m = z (z + 1) ... (z + m - 1)\]See [dlmf] for more details.
- Parameters:
- z, marray_like
Real-valued arguments.
- outndarray, optional
Optional output array for the function results
- Returns:
- scalar or ndarray
The value of the function.
Notes
poch
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
✅
✅
Dask
✅
n/a
See Support for the array API standard for more information.
References
[dlmf]Nist, Digital Library of Mathematical Functions https://dlmf.nist.gov/5.2#iii
Examples
>>> import scipy.special as sc
It is 1 when m is 0.
>>> sc.poch([1, 2, 3, 4], 0) array([1., 1., 1., 1.])
For z equal to 1 it reduces to the factorial function.
>>> sc.poch(1, 5) 120.0 >>> 1 * 2 * 3 * 4 * 5 120
It can be expressed in terms of the gamma function.
>>> z, m = 3.7, 2.1 >>> sc.poch(z, m) 20.529581933776953 >>> sc.gamma(z + m) / sc.gamma(z) 20.52958193377696