Some Fermatian inversion formulae

A. G. Shannon
Notes on Number Theory and Discrete Mathematics, ISSN 1310-5132
Volume 13, 2007, Number 4, Pages 7—10
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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 q-extensions of binomial coefficients formed from rising factorial coefficients. Some of the results are applied to a Möbius Inversion Formula and an exponential based on extensions of ideas initially developed by Leonard Carlitz.


  • q-series
  • Fermatian functions
  • Binomial coefficients
  • Möbius function
  • Rising factorials
  • Hermite polynomials

AMS Classification

  • 11B65
  • 11B39
  • 05A30


  1. Carlitz, L. q-Bernoulli Numbers and Polynomials. Duke Mathematical Journal. 15, 1948, 987-1000.
  2. Carlitz, L. Expansions of q-Bernoulli Numbers. Duke Mathematical Journal. 25, 1958, 355-364.
  3. Carlitz, L. Extended Bernoulli and Eulerian Numbers. Duke Mathematical Journal 31, 1964, 667-690.
  4. Jia. C.Z., H.M. Liu, T.M. Wang, q-analogs of Generalized Fibonacci and Lucas Polynomials. The Fibonacci Quarterly. 451, 2007, 26-34.
  5. Shannon, AG. Some Generalized Binomial Coefficients. Notes on Number Theory and Discrete Mathematics. 13, 1, 2007, 25-30.
  6. Shannon, AG. Some q-Series Inversion Formulae. Notes on Number Theory and Discrete Mathematics. 13, 2, 2007, 15-18.

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Cite this paper

Shannon, A. G. (2007). Some Fermatian inversion formulae. Notes on Number Theory and Discrete Mathematics, 13(4), 7-10.

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