The reciprocal of the beta function and \(GL(n,R)\) Whittaker functions
type: Item
instance of: scholarly article
title: The reciprocal of the beta function and \(GL(n,R)\) Whittaker functions
zbMATH Open document ID: 0801.33001
author: Eric Stade
publication date: 1994-06-16T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/75062
review text: 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 \(\text{GL} (n,\mathbb{R})\) 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 of ``fundamental'' Whittaker functions for \(\text{GL}(3,\mathbb{R})\) and \(\text{GL} (4,\mathbb{R})\). The integrals obtained are seen to resemble very closely known integrals for the ``class-one'' Whittaker functions on these groups. It is expected that this correspondence between expressions for different types of Whittaker functions will carry over to groups of arbitrary rank.
Mathematics Subject Classification ID: 33B15
Mathematics Subject Classification ID: 11F30
Mathematics Subject Classification ID: 43A85
zbMATH DE Number: 566965
zbMATH Keywords: automorphic forms
zbMATH Keywords: beta function
zbMATH Keywords: Whittaker functions
MaRDI profile type: Publication
OpenAlex ID: W2325711322
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DOI: 10.5802/AIF.1390
published in: Annales de l’institut Fourier
description: scientific article; zbMATH DE number 566965