scipy.special.beta#
- scipy.special.beta(a, b, out=None) = <ufunc 'beta'>#
Beta function.
This function is defined in [1] as
\[B(a, b) = \int_0^1 t^{a-1}(1-t)^{b-1}dt = \frac{\Gamma(a)\Gamma(b)}{\Gamma(a+b)},\]where \(\Gamma\) is the gamma function.
- Parameters
- a, barray-like
Real-valued arguments
- outndarray, optional
Optional output array for the function result
- Returns
- scalar or ndarray
Value of the beta function
See also
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 \(B(1, b) = 1/b\):
>>> sc.beta(1, 4) 0.25