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

Yilmaz Simsek ()
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Yilmaz Simsek: University of Akdeniz Faculty Science, Department of Mathematics

A chapter in Analytic Number Theory, Approximation Theory, and Special Functions, 2014, pp 149-214 from Springer

Abstract: 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.

Keywords: Zeta Function; Bernoulli Number; Bernoulli Polynomial; Dirichlet Character; Hurwitz Zeta Function (search for similar items in EconPapers)
Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4939-0258-3_6

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DOI: 10.1007/978-1-4939-0258-3_6

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