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