Some generalized rising binomial coefficients

A. G. Shannon
Notes on Number Theory and Discrete Mathematics, ISSN 1310–5132
Volume 13, 2007, Number 1, Pages 25–30
Full paper (PDF, 95 Kb)


Authors and affiliations

A. G. Shannon
Warrane College, The University of New South Wales, Kensington 1465, &
Raffles KvB, 99 Mount Street, North Sydney, NSW 2065, Australia


This paper considers some properties of generalized binomial coefficients which are defined in terms of rising factorial coefficients. Analogies with classical results in number theory and some generalized special functions are highlighted.


  • q-series
  • Binomial coefficients
  • Rising factorials
  • Generalized Fibonacci numbers
  • Appell set
  • Gauss–Cayley generalizations.

AMS Classification

  • 11B65
  • 11B39
  • 05A30


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Cite this paper

Shannon, A. G. (2007). Some generalized rising binomial coefficients. Notes on Number Theory and Discrete Mathematics, 13(1), 25-30.

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