Ramanujan's master theorem for symmetric cones
type: Item
instance of: scholarly article
title: Ramanujan's master theorem for symmetric cones
zbMATH Open document ID: 0880.33013
author: Hongming Ding
author: Kenneth I. Gross
author: Donald Richards
published in: Pacific Journal of Mathematics
publication date: 1998-02-08T00:00:00Z
review text: Ramanujan's Master Theorem from 1913, which relates coefficients in the Taylor expansion of a function to the Mellin transform of the function over the interval \((0,\infty)\), is generalized to symmetric cones in the paper under review. An outline of the paper follows. The first part is mainly expository, dealing at some length with the necessary background material on symmetric cones, Jordan algebras, and harmonic analysis on symmetric cones, including Pochhammer symbol, gamma function, zonal polynomials, spherical functions, and Plancherel's formula. Then after introducing Hardy classes, the authors prove the Master Theorem. The classical case is first considered and then the rather long proof for the symmetrical cone case follows. In the final sections the authors study further subjects connected with the theorem: Newton's interpolation formula, generalized binomial coefficients, Mellin-Barnes integrals, and hypergeometric series.
Mathematics Subject Classification ID: 33C80
Mathematics Subject Classification ID: 44A15
zbMATH DE Number: 1026457
zbMATH Keywords: hypergeometric functions
zbMATH Keywords: Jordan algebras
zbMATH Keywords: Mellin-Barnes integrals
reviewed by: Hitoshi Abe
MaRDI profile type: Publication
full work available at URL: pjm.1996.175.447
OpenAlex ID: W1525990648
DOI: 10.2140/PJM.1996.175.447
description: scientific article; zbMATH DE number 1026457