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Author
D. Veestraeten
Year
2017
Title
An alternative integral representation for the product of two parabolic cylinder functions
Journal
Integral Transforms and Special Functions
Volume | Issue number
28 | 12
Pages (from-to)
915-922
Number of pages
8
Document type
Article
Faculty
Faculty of Economics and Business (FEB)
Institute
Amsterdam School of Economics Research Institute (ASE-RI)
Abstract
Recently, [Veestraeten D. An integral representation for the product of parabolic cylinder functions. Integral Transforms Spec Funct. 2017;28(1):15–21] derived an integral representation for Dν(x)Dμ(y) with Re(ν+μ)<1 that was expressed in terms of the Gaussian hypergeometric function. This paper obtains an alternative expression for Dν(x)Dμ(y) in which the integrand contains the parabolic cylinder function itself with the condition for convergence being at Re(ν)<0. The latter property is subsequently used to generate a new integral representation for Dμ(y) in which restrictions on the order μ are absent.
URL
go to publisher's site
Language
English
Permalink
http://hdl.handle.net/11245.1/f61c3ffb-c27d-46db-a86e-a3f46f8fa595
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  • An alternative integral representation

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