Module « scipy.special »

Fonction beta - module scipy.special

Signature de la fonction beta

Description

beta.__doc__

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

beta(a, b, out=None)

Beta function.

This function is defined in [1]_ as

.. math::

    B(a, b) = \int_0^1 t^{a-1}(1-t)^{b-1}dt
            = \frac{\Gamma(a)\Gamma(b)}{\Gamma(a+b)},

where :math:`\Gamma` is the gamma function.

Parameters
----------
a, b : array-like
    Real-valued arguments
out : ndarray, optional
    Optional output array for the function result

Returns
-------
scalar or ndarray
    Value of the beta function

See Also
--------
gamma : the gamma function
betainc :  the incomplete beta function
betaln : the natural logarithm of the absolute
         value of the beta function

References
----------
.. [1] NIST Digital Library of Mathematical Functions,
       Eq. 5.12.1. https://dlmf.nist.gov/5.12

Examples
--------
>>> import scipy.special as sc

The beta function relates to the gamma function by the
definition given above:

>>> sc.beta(2, 3)
0.08333333333333333
>>> sc.gamma(2)*sc.gamma(3)/sc.gamma(2 + 3)
0.08333333333333333

As this relationship demonstrates, the beta function
is symmetric:

>>> sc.beta(1.7, 2.4)
0.16567527689031739
>>> sc.beta(2.4, 1.7)
0.16567527689031739

This function satisfies :math:`B(1, b) = 1/b`:

>>> sc.beta(1, 4)
0.25