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