We have used the idea of ‘quasi inner product’ introduced by L. R.
Bragg in 1986 to consider generating series
∑n=0∞Hn2(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.