# 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, 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 regularized 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 \(B(1, b) = 1/b\):

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