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Gamma, Beta, Erf > Gamma[z] > Introduction to the Gamma Function

Definition of gamma function

The gamma function in the half-plane is defined as the value of the following definite integral:

This integral is an analytic function that can be represented in different forms; for example, as the following sum of an integral and a series without any restrictions on the argument:

The last formula can also be used as an equivalent definition of the gamma function.