Gamma function
Extension of the factorial function
Gamma function
In mathematics, the gamma function, denoted by Γ {\displaystyle \Gamma } (capital Greek letter gamma), is the most common extension of the factorial function to complex numbers. First studied by Daniel Bernoulli, the gamma function is defined for all complex numbers z {\displaystyle z} except non-positive integers, and satisfies Γ ( n ) = ( n − 1 ) ! {\displaystyle \Gamma (n)=(n-1)!} for every positive integer n {\displaystyle n} . The gamma function can be defined via a convergent improper integral for complex numbers with positive real part: Γ ( z ) = ∫ 0 ∞ t...
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