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Gamma-function

[ G- function, F(.x) ], one of the most important special functions, which generalizes the concept of factorial; for positive integer n it is equal is for the first time introduced By l. Euler into 1729. G.- f. for real x > 0 is determined by the equality

another designation:

Fundamental Relationships For G.- f.:

Particular values:

With large X is valid asimptotich. Sterling the formula

The large number of definite integrals is expressed through G.- f., infinite works and sums it is series. G.- f. is extended also to the complex values of argument.

Lit.: To yanke e., To emde f., the table of functions with the formulas and the curves, translated from the German, 3 publ., M., 1959; Fikhtengol'ts g. M., the course of differential and integral calculus, 6 publ., Vol. 2, M., 1966.

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