Some formule involving Hermite polynomial, confluent hypergeometric function and Meijer's G-function



Abstract

In this paper, we evaluate two integrals involving Hermite polynomial and confluent hypergeometric function, and employ one of them to evaluate an integral involving Meijer's G-function. We use the integral involving Meijer's G-function to evaluate a double integral involving Meijer's G-function. We further employ the integral involving Meijer's G-function to establish one one-dimensional Fourier-Hermite expansion and one two-dimensional Fourier-Hermite expansion. We also obtain a solution of a heat conduction problem.


1. L.C. Andrews, Special functions for engineers and applied mathematicians, Macmillan Publishing Co., New York 1985.
2. S.D. Bajpai, An expansion formula for Meijer's G-function involving Hermite polynomials, Lab. J. Sci. Tech., 8-A No. 1 (1970), 9-11.
3. B.R. Bhonsle, Heat conduction and Hermite polynomials, Proc. Nat. Acad. Sci. India Sect. A, 36A (1966), 359-360.
4. R.V. Churchill, Operational Mathematics, McGraw-Hill, New York 1958.
5. A. Erdélyi et al., Higher transcendental functions, Vol. 1, McGraw-Hill, New York 1953.
6. A. Erdélyi et al., Tables of integral transforms, Vol. 2, McGraw-Hill, New York 1954.
7. I.S. Gradshteyn, I.M. Ryzhik, Tables of integrals, series, and products, Academic Press, Inc., New York 1980.
8. J. Kampé de Fériet, Heat conduction and Hermite polynomials, Bull. Calcutta Math. Soc., Golden Jubilee Commemoration Volume (1958-1959), 193-204.
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Published : 1992-09-30


BajpaiS. D. (1992). Some formule involving Hermite polynomial, confluent hypergeometric function and Meijer’s G-function. Annales Mathematicae Silesianae, 6, 13-20. Retrieved from https://journals.us.edu.pl/index.php/AMSIL/article/view/14262

Shri Dhar Bajpai 
Department of Mathematics, University of Bahrain  Bahrain



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