Remarks on a generalized beta function
نویسنده
چکیده
We show that a certain generalized beta function B(x; y; b) which reduces to Euler’s beta functions B(x; y) when its variable b vanishes and preserves symmetry in its parameters may be represented in terms of a nite number of well known higher transcendental functions except (possibly) in the case when one of its parameters is an integer and the other is not. In the latter case B(x; y; b) may be represented as an in nite series of either Wittaker functions or Laguerre polynomials. As a byproduct of this investigation we deduce representations for several in nite series containing Wittaker functions, Laguerre polynomials, and products of both. c © 1998 Elsevier Science B.V. All rights reserved. AMS classi cation: 33B15; 33B99; 33C15; 33C45
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