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Formulas of the dirichlet-mehler type

Part of the Lecture Notes in Mathematics book series (LNM,volume 457)

Abstract

A fractional integral formula of Erdélyi is used to show that the fractional calculus leads in a natural way to useful formulas of the Dirichlet-Mehler type for the Jacobi polynomials and the generalized Legendre functions. Some important applications are pointed out, and a discrete analogue of Erdélyi's formula is derived and used to obtain a discrete Dirichlet-Mehler type formula for the Hahn polynomials (a discrete analogue of the Jacobi polynomials).

Keywords

  • Fractional Calculus
  • Legendre Polynomial
  • Jacobi Polynomial
  • Discrete Analogue
  • Jacobi Function

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Supported in part by NSF Grant GP-32116. The author is an Alfred P. Sloan fellow.

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© 1975 Springer-Verlag

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Gasper, G. (1975). Formulas of the dirichlet-mehler type. In: Ross, B. (eds) Fractional Calculus and Its Applications. Lecture Notes in Mathematics, vol 457. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0067105

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  • DOI: https://doi.org/10.1007/BFb0067105

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  • Print ISBN: 978-3-540-07161-7

  • Online ISBN: 978-3-540-69975-0

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