**A. G. Shannon**

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

Volume 9, 2003, Number 4, Pages 73–82

**Full paper (PDF, 101 Kb)**

## Details

### Authors and affiliations

**A. G. Shannon**

*Warrane College, The University of New South Wales, 1465,
& KvB Institute of Technology, North Sydney, 2060, Australia
*

### Abstract

Generalizations of the polynomials of Bernoulli, Euler and Hermite are defined here in terms of generalized integers called Fermatian integers. These are closely related to the q-series extensively studied by Leonard Carlitz. These various analogues of the classical special functions are inter-related with one another and also to some of the problems posed by Morgan Ward. The works of Henry Gould and Vern Hoggatt are also extensively cited.

### AMS Classification

- 11B65
- 11B68
- 11B39

### References

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## Related papers

- Shannon, A. G. (2003). Generalized Bernoulli Polynomials and Jackson’s Calculus of Sequences.
*Notes on Number Theory & Discrete Mathematics*, 9(1), 1-6.

## Cite this paper

Shannon, A. G. (2003). Some Fermatian special functions. *Notes on Number Theory and Discrete Mathematics*, 9(4), 73-82.