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The gamma function, is
The gamma function can be thought of as the extension of the
factorial to the entire real (or complex) number set. For non-negative integers
it is merely the familiar factorial function, , but offset by 1,
Like factorials, it satisfies the following recurrence relationship:
The Nematrian website approximates the gamma function using
a so-called Lanczos
approximation, see also Press et
al. (2007), Toth (2004) or
The particular Lanczos approximation the Nematrian website
For large there is a risk of overflow, which can
be mitigated by using the MnLogGamma
function, defined as .
The Lanczos approximation is valid for arguments in the
right complex half-plane, but can be extended to the entire complex plane
(where the function is not singular) using the reflection formula, i.e.
See also MnCGamma.
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Interactively run function
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