A. G. Shannon
Notes on Number Theory and Discrete Mathematics, ISSN 1310-5132
Volume 13, 2007, Number 2, Pages 15—18
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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 based on extensions of ideas initially developed by Leonard Carlitz.
Keywords
- q-series
- Binomial coefficients
- Möbius function
- Rising factorials
- Exponential functions
AMS Classification
- 11B65
- 11B39
- 05A30
References
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- Carlitz, L. Characterization of Certain Sequences of Orthogonal Polynomials. Portugaliae Mathematica. 20 (1961): 43-46.
- Carlitz, L. Generating Functions for Powers of Certain Sequences of Numbers. Duke Mathematical Journal. 29 (1962): 521-537.
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- Cauchy, A.L. Memoire sur les functions don plusiers valuers. Comptes Rendus de l’Academie des Sciences. 17 (1843): 526-534.
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- Kim, T. & S.H. Rim. On Changed q-Euler Numbers and Polynomials. Advanced Studies in Contemporary Mathematics. 9 (2004): 81-86.
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Cite this paper
Shannon, A. G. (2007). Some q-series inversion formulae. Notes on Number Theory and Discrete Mathematics, 13(2), 15-18.