Some results on quasi-monomiality

  • Authors:

  • Youssèf Ben Cheikh

  • Affiliations:

  • Département de Mathématiques, Faculté des Sciences, Ecole Ntnl D'Ingenieurs de Monastir, 5019 Monastir, Tunisia

  • Venue:
  • Applied Mathematics and Computation - Special issue: Advanced special functions and related topics in differential equations, third Melfi workshop, proceedings of the Melfi school on advanced topics in mathematics and physics
  • Year:
  • 2003

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Abstract

A polynomial set { P n } n ≥0 is called quasi-monomial if and only if it is possible to define two operators P and M , independent of n , such that P(P n )(x) = nP n -1 ( x ) and M (P n )(x) = P n +1 ( x ). In this paper, we show that every polynomial set is quasi-monomial and we present some useful tools to explicitly express the P and M operators for some polynomial families given by their generating functions. The obtained results are applied to Boas-Buck polynomial sets.