A. G. Shannon

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

Volume 14, 2008, Number 1, Pages 1—5

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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 considers some properties of rising binomial coefficients and two analogs of the Bernoulli polynomials which can be developed from them.

### Keywords

*q*-series- Binomial coefficients
- Rising factorials
- Generalized Bernoulli polynomials
- Gauss-Cayley generalizations
- Fermatians

### AMS Classification

- 11B65
- 11B39
- 05A30

### References

- Carlitz, L.
*q*-Bernoulli Numbers and Polynomials.*Duke Mathematical Journal*. 16 (1949): 987-1000. - Carlitz, L. Generating Functions.
*The Fibonacci Quarterly*. Vol.7 (1969): 359-393. - Dyson, F. A Walk through Ramanujan’s Garden. In George E Andrews
*et al*(eds).*Ramanujan Revisited*. San Diego, CA: Academic Press, pp.7-28. - Ismail, Mourad.
*Classical and Quantum Orthogonal Polynomials in One Variable.*Encyclopedia of Mathematics and Its Applications, 98. Cambridge: Cambridge University Press. - Riordan, J.
*An Introduction to Combinatorial Analysis*. New York: Wiley, 1958, p.3. - Riordan, J. Abel Identities and Inverse Relations. In
*Combinatorial Mathematics and Its Applications*. Chapel Hill, NC: University of North Carolina Press, pp.71-92. - Shannon, A.G. Some
*q*-Binomial Coefficients Formed from Rising Factorials.*Notes on Number Theory and Discrete Mathematics.*12 (2006): 13-20. - Sylvester, J.J.
*The Collected Mathematical Papers of James Joseph Sylvester.*Volume IV (1882-1897). New York: Chelsea, 1973, pp.91,93-94.

## Related papers

## Cite this paper

APAShannon A. G. (2008). Rising factorial Bernoulli polynomials. Notes on Number Theory and Discrete Mathematics, 14(1), 1-5.

ChicagoShannon, AG. “Rising Factorial Bernoulli Polynomials.” Notes on Number Theory and Discrete Mathematics 14, no. 1 (2008): 1-5.

MLAShannon, AG. “Rising Factorial Bernoulli Polynomials.” Notes on Number Theory and Discrete Mathematics 14.1 (2008): 1-5. Print.