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Generating functions of the twisted Bernoulli numbers and polynomials associated with their interpolation functions

Yilmaz Simsek
장전수학회 (Jangjeon Mathematical Society)|2008.04|Advanced Studies in Contemporary Mathematics|제16권 제2호|pp. 251-278

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참고문헌

키워드

q-Bernoulli numbers and polynomialsL-functiontwistedq-Bernoullinumbers and polynomialsq- zeta functiontwistedq-zeta functiontwistedq-L-functionsq-Volkenborn integral.
주제분류수학

초록

The main purpose of this paper is to study on generating functions of the twisted (q-)Bernoulli numbers, polynomials and their interpolation functions. Relations between thesegenerating functions and (q-) Volkenborn integral are studied. By applying the Mellintransformation to these generating functions, we construct twisted (q-analogue) Riemannzeta function, twisted (q-analogue) Hurwitz zeta function, twisted (q-analogue) DirichletL-function and twisted two-variable (q-analogue)L-function, which are interpolated twisted(q-) Bernoulli numbers and twisted (q-) Bernoulli polynomials at non-positive integers, re-spectively. Furthermore, we nd distribution relations of generalized twisted Bernoulli num-bers and polnomials.

Abstract

The main purpose of this paper is to study on generating functions of the twisted (q-)Bernoulli numbers, polynomials and their interpolation functions. Relations between thesegenerating functions and (q-) Volkenborn integral are studied. By applying the Mellintransformation to these generating functions, we construct twisted (q-analogue) Riemannzeta function, twisted (q-analogue) Hurwitz zeta function, twisted (q-analogue) DirichletL-function and twisted two-variable (q-analogue)L-function, which are interpolated twisted(q-) Bernoulli numbers and twisted (q-) Bernoulli polynomials at non-positive integers, re-spectively. Furthermore, we nd distribution relations of generalized twisted Bernoulli num-bers and polnomials.

참고문헌 (40)

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