Mellin transforms of Whittaker functions on GL(4, R) and GL(4, C).
The reciprocal of the beta function and Whittaker functions
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 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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