Affiliation:
1. Tandis Hospital,Tehran
Abstract
Abstract
This paper presents the connections between univariate and bivariate Hermite polynomials and associated differential equations with specific representations of 𝔰𝔩(2,𝑅) algebra whose Cartan sub-algebras coincide with the differential operators involved in these differential equations . 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 𝔰𝔩(2,𝑅) representation for other special polynomials such as Laguerre and Legendre polynomials is introduced. A new generating function for Hermite polynomials is presented.
Publisher
Research Square Platform LLC
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