An integral representation for the product of parabolic cylinder functions. Issue 1 (2nd January 2017)

• Record Type: Journal Article
• Authors: Veestraeten, D.
• Is Part Of: Integral transforms and special functions. Volume 28:Issue 1(2017)
• Page Start: 15
• Page End: 21
• Publication Date: 2017-01-02
• Subjects: Associated Legendre function -- convolution theorem -- Gaussian hypergeometricfunction -- integral representation -- inverse Laplace transform -- parabolic cylinder function; 33B20 -- 33C05 -- 33C65 -- 44A10 -- 44A20; Integral transforms -- Periodicals; Transcendental functions -- Periodicals; Transformations (Mathematics) -- Periodicals; Calculus, Integral -- Periodicals; 515
• DOI: 10.1080/10652469.2016.1247837
• Languages: English
• ISSNs: 1065-2469

Abstract

ABSTRACT: This paper uses the convolution theorem of the Laplace transform to derive an inverse Laplace transform for the product of two parabolic cylinder functions in which the orders as well as the arguments differ. This result subsequently is used to obtain an integral representation for the product of two parabolic cylinder functionsD ν ( x ) D μ ( y ) . The integrand in the latter representation contains the Gaussian hypergeometric function or alternatively can be expressed in terms of the associated Legendre function of the first kind.