Generalized Bernoulli polynomials & Jackson’s calculus of sequences

A. G. Shannon
Notes on Number Theory and Discrete Mathematics, ISSN 1310-5132
Volume 9, 2003, Number 1, Pages 1—6
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Authors and affiliations

A. G. Shannon
Warrane College, The University of New South Wales
Kensington 1465, & KvB Institute of Technology, North Sydney, NSW 2060, Australia


This paper considers generalized Bernoulli and exponential functions in the context of factorials formed from the elements of divisibility sequences as in the calculus of sequences of Jackson and Ward. The results for the ordinary integers readily follow. Suggestions for further relevant research with commutative diagrams are included.

AMS Classification

  • 11B39
  • 11B65
  • 11B686


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Cite this paper

Shannon, A. (2003). Generalized Bernoulli polynomials & Jackson’s calculus of sequences. Notes on Number Theory and Discrete Mathematics, 9(1), 1-6.

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