Fermatian analogues of Gould’s generalized Bernoulli polynomials

A. G. Shannon
Notes on Number Theory and Discrete Mathematics, ISSN 1310–5132
Volume 16, 2010, Number 4, Pages 14–17
Full paper (PDF, 117 Kb)

Details

Authors and affiliations

A. G. Shannon
Warrane College, The University of New South Wales,
PO Box 123, Kensington, NSW 1465, Australia

Abstract

Some results of Gould for the ordinary Bernoulli and Euler polynomials are extended to analogous results built upon the Fermatian exponentials.

Keywords

• Fermatian numbers
• Fibonacci numbers
• Bernoulli polynomials
• Euler 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. Gould, H.W. Generating Functions for Products of Fibonacci Numbers. The Fibonacci Quarterly. 1 (2), 1963: 1-16.
4. Gould, H.W. Binomial Coefficients, the Bracket Function, and Compositions with Relatively Prime Summands. The Fibonacci Quarterly. 2 (1964): 241-260.
5. Gould, H.W. Remarks on Compositions of Numbers into Relatively Prime Parts. Notes on Number Theory and Discrete Mathematics. 11(3) (2005): 1-6.
6. Hoggatt, Verner E., Jr. Fibonacci Numbers and Generalized Binomial Coefficients. The Fibonacci Quarterly. 5 (4), 1967: 383-400.
7. Shannon, A.G. Some Fermatian Inversion Formulae. Notes on Number Theory and Discrete Mathematics. 13 (4), 2007: 7-10.
8. Vorobev, N.N. Fibonacci Numbers. Oxford: Pergamon.