Gamma
[this page  pdf  references  back links]
Function Description
The gamma function, is
defined as:
The gamma function can be thought of as the extension of the
factorial to the entire real (or complex) number set. For nonnegative integers
it is merely the familiar factorial function, , but offset by 1,
i.e. .
Like factorials, it satisfies the following recurrence relationship:
The Nematrian website approximates the gamma function using
a socalled Lanczos
approximation, see also Press et
al. (2007), Toth (2004) or
Wikipedia:
Lanczos approximation.
The particular Lanczos approximation the Nematrian website
uses involves:
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 halfplane, but can be extended to the entire complex plane
(where the function is not singular) using the reflection formula, i.e.
See also MnCGamma.
NAVIGATION LINKS
Contents  Prev  Next
Links to:

Interactively run function

Interactive instructions

Example calculation

Output type / Parameter details

Illustrative spreadsheet

Other Special Functions

Computation units used
Note: If you use any Nematrian web service either programmatically or interactively then you will be deemed to have agreed to the Nematrian website License Agreement