Hypergeometric functions as a tool for summability of the Fourier integral
type: Item
instance of: scholarly article
title: Hypergeometric functions as a tool for summability of the Fourier integral
zbMATH Open document ID: 0908.33003
DOI: 10.1007/BF03322038
published in: Results in Mathematics
publication date: 1999-03-18T00:00:00Z
review text: This paper is essentially a sequel to an earlier work by the first-named author and \textit{Y. Xu} [Math. Proc. Camb. Philos. Soc. 122, No. 1, 149-172 (1997; Zbl 0881.42007)] in which the so-called \(\ell-1\) summability of the inverse Fourier integral on \(\mathbb{R}^a\) was studied and a pair of Fourier kernels \(\{h_d,m_d\}\) on \(\mathbb{R}_+\) was introduced as the core of the summability scheme. In this paper, these same kernels are investigated once again from the point of view of special functions. The authors rederive several basic properties of these Fourier kernels. In particular, they derive a power series expansion verifying Ramanujan's master theorem.
Mathematics Subject Classification ID: 33C20
Mathematics Subject Classification ID: 42B08
Mathematics Subject Classification ID: 42B10
zbMATH DE Number: 1209930
author: Hubert Berens
author: Wolfgang zu Castell
reviewed by: H. M. Srivastava
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf03322038
OpenAlex ID: W2050494254
description: scientific article; zbMATH DE number 1209930