A. G. Shannon

Notes on Number Theory and Discrete Mathematics, ISSN 1310-5132

Volume 14, 2008, Number 1, Pages 6—9

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## Details

### Authors and affiliations

A. G. Shannon

*Warrane College, The University of New South Wales, Kensington 1465, &
Raffles College, 99 Mount Street, North Sydney, NSW 2065, Australia
*

### Absrtacts

This paper utilized a modification of *q*-series to develop some partition formulas in the tradition of Bernoulli—Euler—Rogers—Ramanujan identities. Many of the ideas owe their development to the detailed pioneering work of Leonard Carlitz, with the added acknowledgement to the creative work currently being done by other number theorists working in this fertile area.

### AMS Classification

- 11B65
- 11B39
- 05A30

### References

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*Bolletino della Unione Matematica Italiana.*(4) 1 (1968): 362-365. - Carlitz, L. A Note on the Rogers-Ramanujan Identities.
*Duke Mathematical Journal*. 35 (1968): 839-842.Carlitz, L. Fibonacci Representations. II.*The Fibonacci Quarterly.*8 (1970): 113-134. - Carlitz, L. Some Identities in Combinatorial Analysis.
*Duke Mathematical Journal*. 38 (1971): 51-56. - Ernst, T. Examples of a
*q*-umbral Calculus.*Advanced Studies in Contemporary Mathematics.*16 (2008): 1-22. - Kim, T. Some Formulae for the
*q*-Bernoulli and Euler Polynomials.*Journal of Mathematical Analysis and Applications*. 273 (2002): 236-242. - Kim, T. Analytic Continuation of Multiple
*q*-zeta Functions and their Values at Negative Integers.*Russian Journal of Mathematics & Physics.*11 (2004): 71-76. - Kim, T. & S.H. Rim. On Changed
*q*-Euler Numbers and Polynomials.*Advanced Studies in Contemporary Mathematics*. 9 (2004): 81-86. - Sylvester, J.J.
*The Collected Mathematical Papers of James Joseph Sylvester.*Volume IV (1882-1897). New York: Chelsea, 1973, pp.91,93-94.

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## Cite this paper

Shannon A. G. (2008). A *q*-series Bernoulli—Euler partition formula. Notes on Number Theory and Discrete Mathematics, 14(1), 6-9.