scipy.special.poch — SciPy v1.15.2 Manual (original) (raw)

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.

References

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