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. 
 
 - 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