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Associated Lie Algebras of One-Variable and Bivariate Hermite Polynomials and New Generating Functions
Version 1
: Received: 17 March 2023 / Approved: 20 March 2023 / Online: 20 March 2023 (02:18:57 CET)
How to cite: Amiri, M. Associated Lie Algebras of One-Variable and Bivariate Hermite Polynomials and New Generating Functions. Preprints 2023, 2023030332. https://doi.org/10.20944/preprints202303.0332.v1 Amiri, M. Associated Lie Algebras of One-Variable and Bivariate Hermite Polynomials and New Generating Functions. Preprints 2023, 2023030332. https://doi.org/10.20944/preprints202303.0332.v1
Abstract
This paper presents the symmetries of differential equations associated with one-variable and Bivariate Hermite polynomials by proposing a representation of Lie algebra for these differential operators. Applying the Baker-Campbell-Hausdorff formula to these algebras, results in new relations and generating functions in one-variable and Bivariate Hermite polynomials. A general form of representation for other orthogonal polynomials such as Laguerre polynomials is introduced.
Keywords
Bivariate Hermite Polynomial; Lie Algebra; Baker-Campbell-Hausdorff formula; generating function; sl (2,R) algebra
Subject
Computer Science and Mathematics, Mathematics
Copyright: 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.
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