jax.scipy.special.gamma — JAX documentation (original) (raw)

jax.scipy.special.gamma#

jax.scipy.special.gamma(x)[source]#

The gamma function.

JAX implementation of scipy.special.gamma.

The gamma function is defined for \(\Re(z)>0\) as

\[\mathrm{gamma}(z) = \Gamma(z) = \int_0^\infty t^{z-1}e^{-t}\mathrm{d}t\]

and is extended by analytic continuation to arbitrary complex values z. For positive integers n, the gamma function is related to thefactorial() function via the following identity:

\[\Gamma(n) = (n - 1)!\]

• if \(z = -\infty\), NaN is returned.
• if \(x = \pm 0\), \(\pm \infty\) is returned.
• if \(x\) is a negative integer, NaN is returned. The sign of gamma at a negative integer depends on from which side the pole is approached.
• if \(x = \infty\), \(\infty\) is returned.
• if \(x\) is NaN, NaN is returned.

Parameters:

x (ArrayLike) – arraylike, real valued.

Returns:

array containing the values of the gamma function

Return type:

Array

See also

• jax.scipy.special.factorial(): the factorial function.
• jax.scipy.special.gammaln(): the natural log of the gamma function
• jax.scipy.special.gammasgn(): the sign of the gamma function

Notes

Unlike the scipy version, JAX’s gamma does not support complex-valued inputs.