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Gamma Function

  Euler's gamma function is defined by the integral

For real integer and half integer arguments it is given by

and the recurrence formula valid for all complex z (except negative integers and zero) is

Some further values of the Gamma function for small arguments are:

(1/5)=4.5909 (1/4)=3.6256
(1/3)=2.6789 (2/5)=2.2182
(3/5)=1.4892 (2/3)=1.3541
(3/4)=1.2254 (4/5)=1.1642 .

An asymptotic formula for and |z| large is Stirling's formula

which also approximates the factorial:

Rudolf K. Bock, 7 April 1998