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