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