scipy.special.poch

scipy.special.poch(z, m) = <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.

Returns

scalar or ndarray

The value of the function.

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