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Families of Twisted Bernoulli Numbers, Twisted Bernoulli Polynomials, and Their Applications

In: Analytic Number Theory, Approximation Theory, and Special Functions

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  • Yilmaz Simsek

    (University of Akdeniz Faculty Science, Department of Mathematics)

Abstract

This chapter is motivated by the fact that the theories and applications of the many methods and techniques used in dealing with some different families of the twisted Bernoulli numbers, the twisted Bernoulli polynomials, and their families of interpolation functions, which are the family of twisted zeta functions, the family of twisted L-functions. By using the p-adic Volkenborn integral, twisted (h, q)-Bernoulli numbers and twisted (h, q)-Bernoulli polynomials are introduced. The p-adic meromorphic functions, which interpolation twisted (h, q)-Bernoulli numbers and twisted (h, q)-Bernoulli polynomials, associated with the p-adic Volkenborn integral, are presented. Furthermore relationships between Bernoulli functions, Euler functions, some arithmetic sums, Dedekind sums, Hardy Berndt sums, DC-sums, trigonometric sums, and Hurwitz zeta function are given.

Suggested Citation

  • Yilmaz Simsek, 2014. "Families of Twisted Bernoulli Numbers, Twisted Bernoulli Polynomials, and Their Applications," Springer Books, in: Gradimir V. Milovanović & Michael Th. Rassias (ed.), Analytic Number Theory, Approximation Theory, and Special Functions, edition 127, pages 149-214, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4939-0258-3_6
    DOI: 10.1007/978-1-4939-0258-3_6
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