Evaluation of Certain Integrals Involving the Product of Classical Hermite's Polynomials Using Laplace Transform Technique and Hypergeometric Approach
Year: 2017
Analysis in Theory and Applications, Vol. 33 (2017), Iss. 4 : pp. 355–365
Abstract
In this paper some novel integrals associated with the product of classical Hermite’s polynomials $$\int^{+∞}_{−∞} (x^2)^m exp(−x^2)\{H_r(x)\}^2dx,\ \int^∞_0 exp(−x^2)H_{2k} (x)H_{2s+1}(x)dx,$$ $$\int^∞_0 exp(−x^2 )H_{2k}(x)H_{2s}(x)dx \ \text{and}\ \int^∞_0 exp(−x^2)H_{2k+1}(x)H_{2s+1}(x)dx,$$ are evaluated using hypergeometric approach and Laplace transform method, which is a different approach from the approaches given by the other authors in the field of special functions. Also the results may be of significant nature, and may yield numerous other interesting integrals involving the product of classical Hermite’s polynomials by suitable simplifications of arbitrary parameters.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/ata.2017.v33.n4.5
Analysis in Theory and Applications, Vol. 33 (2017), Iss. 4 : pp. 355–365
Published online: 2017-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 11
Keywords: Gauss’s summation theorem classical Hermite’s polynomials generalized hypergeometric function generalized Laguerre’s polynomials.