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The reciprocal of the beta function and G L ( n , ) Whittaker functions

Eric Stade — 1994

Annales de l'institut Fourier

In this paper we derive, using the Gauss summation theorem for hypergeometric series, a simple integral expression for the reciprocal of Euler’s beta function. This expression is similar in form to several well-known integrals for the beta function itself. We then apply our new formula to the study of G L ( n , ) Whittaker functions, which are special functions that arise in the Fourier theory for automorphic forms on the general linear group. Specifically, we deduce explicit integral representations...

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