scipy.special.betaln#

scipy.special.betaln(a, b, out=None) = <ufunc 'betaln'>#

Natural logarithm of absolute value of beta function.

Computes ln(abs(beta(a, b))).

Parameters:

a, barray_like: Positive, real-valued parameters
outndarray, optional: Optional output array for function values

Returns:

scalar or ndarray: Value of the betaln function

See also

gamma: the gamma function
betainc: the regularized incomplete beta function
beta: the beta function

Notes

betaln has experimental support for Python Array API Standard compatible backends in addition to NumPy. Please consider testing these features by setting an environment variable SCIPY_ARRAY_API=1 and providing CuPy, PyTorch, JAX, or Dask arrays as array arguments. The following combinations of backend and device (or other capability) are supported.

Library	CPU	GPU
NumPy	✅	n/a
CuPy	n/a	✅
PyTorch	✅	⛔
JAX	✅	✅
Dask	✅	n/a

See Support for the array API standard for more information.

Examples

>>> import numpy as np
>>> from scipy.special import betaln, beta

Verify that, for moderate values of a and b, betaln(a, b) is the same as log(beta(a, b)):

>>> betaln(3, 4)
-4.0943445622221

>>> np.log(beta(3, 4))
-4.0943445622221

In the following beta(a, b) underflows to 0, so we can’t compute the logarithm of the actual value.

>>> a = 400
>>> b = 900
>>> beta(a, b)
0.0

We can compute the logarithm of beta(a, b) by using betaln:

>>> betaln(a, b)
-804.3069951764146