International Journal of Mathematics and Mathematical Sciences
Volume 20 (1997), Issue 3, Pages 613-615
doi:10.1155/S0161171297000847

Fourier transform of hn(x+p)hn(x−p)

Mourad E. H. Ismail1 and Krzystztof Stempak2

1Department of Mathematics, University of South Florida, Tampa 33620, FL, USA
2Instytut Matematyczny, Polskiej Akademii Nauk, ul. Kopernika 18, Wroclaw 51-617, Poland

Received 17 April 1996; Revised 3 December 1996

Copyright © 1997 Mourad E. H. Ismail and Krzystztof Stempak. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We evaluate Fourier transform of a function with Hermite polynomials involved. An elementary proof is based on a combinatorial formula for Hermite polynomials.