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

Abstract

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