On q-deformed generalized Touchard polynomials

Toufik Mansour, Matthias Schork

Research output: Contribution to journalArticlepeer-review


A q-deformed analog of the generalized Touchard polynomials is considered and the connection to generalized Stirling numbers and Bell polynomials is established. For low order m, the q-deformed generalized Touchard polynomials are shown to be related to q-deformed exponential polynomials (m = 1), q-deformed Laguerre polynomials (m = 2), and q-deformed Bessel polynomials (m = - 1). A recurrence relation for the q-deformed generalized Touchard polynomials is derived, representing a generalization of Spivey's relation.

Original languageEnglish
Pages (from-to)634-645
Number of pages12
JournalIndagationes Mathematicae
Issue number4
StatePublished - 1 Aug 2015

Bibliographical note

Publisher Copyright:
© 2015 Royal Dutch Mathematical Society (KWG).


  • Generalized Stirling numbers
  • Spivey relation
  • Touchard polynomials
  • q-deformation

ASJC Scopus subject areas

  • General Mathematics


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