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A capital Greek gamma of a variable, the factorial extended.
Also known as: Gamma function, Euler gamma function, Capital gamma
The gamma function extends the factorial to all complex numbers except the non-positive integers, and it is offset by one for a historical reason nobody defends: Γ(n) equals (n−1)! rather than n!. That off-by-one is the single most common error in using it.
Denotes the gamma function, the analytic continuation of the factorial to the complex plane.
Contexts: Mathematics
Is offset by one from the factorial: Γ(n) = (n−1)!, a convention due to Legendre that later authors have called an error and kept anyway.
Contexts: Mathematics
Has simple poles at zero and every negative integer, and is never zero anywhere.
Contexts: Mathematics
A capital Greek gamma — a horizontal stroke with a vertical stroke descending from its left end — followed by a bracketed variable.