Module « scipy.special »

Fonction poch - module scipy.special

Signature de la fonction poch

Description

poch.__doc__

poch(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])

poch(z, m)

Pochhammer symbol.

The Pochhammer symbol (rising factorial) is defined as

.. math::

    (z)_m = \frac{\Gamma(z + m)}{\Gamma(z)}

For positive integer `m` it reads

.. math::

    (z)_m = z (z + 1) ... (z + m - 1)

See [dlmf]_ for more details.

Parameters
----------
z, m : array_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