Some Fermatian special functions

A. G. Shannon
Notes on Number Theory and Discrete Mathematics, ISSN 1310-5132
Volume 9, 2003, Number 4, Pages 73—82
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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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  21. F. Horadam & A. G. Shannon, Ward’s Staudt-Clausen Theorem, Mathematica Scandinavica, 29 (1976): 239-250.
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  24. Riordan, Abel Identities and Inverse Relations, Combinatorial Mathematics and Its Applications. Chapel Hill: University of North Carolina Press, 1969, pp.71-92.
  25. G. Shannon, Generalized Bernoulli Polynomials and Jackson’s Calculus of Sequences, Notes on Number Theory & Discrete Mathematics, 9 (2003): 1-6.
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Cite this paper

APA

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

Chicago

Shannon, A. G. “Some Fermatian Special Functions.” Notes on Number Theory and Discrete Mathematics, 9, no. 4 (2003): 73-82.

MLA

Shannon, A. G. “Some Fermatian Special Functions.” Notes on Number Theory and Discrete Mathematics, 9.4 (2003): 73-82. Print.

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