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
Full paper (PDF, 31 Kb)

Details

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

Abstract

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.

Keywords

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

AMS Classification

• 11B65
• 11B39
• 05A30

References

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.