Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

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

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