Series with Hermite polynomials and applications

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Boyadzhiev K. N., DİL A.

PUBLICATIONES MATHEMATICAE-DEBRECEN, vol.80, no.3-4, pp.385-404, 2012 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 80 Issue: 3-4
  • Publication Date: 2012
  • Doi Number: 10.5486/pmd.2012.5072
  • Journal Name: PUBLICATIONES MATHEMATICAE-DEBRECEN
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.385-404
  • Keywords: Hermite polynomials, Laguerre polynomials, harmonic numbers, Fibonacci numbers, exponential numbers, geometric numbers, Stirling numbers of the second kind, binomial transformation, Euler series transformation, generating functions
  • Akdeniz University Affiliated: Yes

Abstract

We obtain a series transformation formula involving the classical Hermite polynomials. We then provide a number of applications using appropriate binomial transformations. Several of the new series involve Hermite polynomials and harmonic numbers, Lucas sequences, exponential and geometric numbers. We also obtain a series involving both Hermite and Laguerre polynomials, and a series with Hermite polynomials and Stirling numbers of the second kind.