mars.tensor.special.gamma

mars.tensor.special.gamma(x, **kwargs)

gamma function.

The gamma function is defined as

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

for \(\Re(z) > 0\) and is extended to the rest of the complex plane by analytic continuation. See [dlmf] for more details.

Parameters

z (array_like) – Real or complex valued argument

Returns

Values of the gamma function

Return type

scalar or ndarray

Notes

The gamma function is often referred to as the generalized factorial since \(\Gamma(n + 1) = n!\) for natural numbers \(n\). More generally it satisfies the recurrence relation \(\Gamma(z + 1) = z \cdot \Gamma(z)\) for complex \(z\), which, combined with the fact that \(\Gamma(1) = 1\), implies the above identity for \(z = n\).

References

dlmf

NIST Digital Library of Mathematical Functions https://dlmf.nist.gov/5.2#E1