# mars.tensor.special.gamma#

mars.tensor.special.gamma(x, **kwargs)[source]#

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