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International Journal of Mathematics and Mathematical Sciences
Volume 14, Issue 4, Pages 737-740

Some formulas of L. Carlitz on Hermite polynomials

Department of Mathematics, University of Calcutta, Calcutta 700 019, India

Received 31 May 1991

Copyright © 1991 Hindawi Publishing Corporation. 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.


We have used the idea of ‘quasi inner product’ introduced by L. R. Bragg in 1986 to consider generating series n=0Hn2(x)Hn2(y)tn22n(n!)2 studied by L. Carlitz in 1963. The pecularity of the series is that there is (n!)2 in the denominator, which has a striking deviation from the usuaI generating series containing n! in the denominator. Our generating function for the said generating series is quite different from that of Carlitz, but somewhat analogous to generating integrals derived by G. N. Watson (Higher Transcendental function Vol.III, P 271-272 for the case of Legendre, Gegenbauer and Jacobi polynomials.