- Author
- 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
- Downloads
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