منابع مشابه
The Arakawa–kaneko Zeta Function and Poly-bernoulli Polynomials
The purpose of this paper is to introduce a generalization of the Arakawa–Kaneko zeta function and investigate their special values at negative integers. The special values are written as the sums of products of Bernoulli and poly-Bernoulli polynomials. We establish the basic properties for this zeta function and their special values.
متن کاملOn Functions of Arakawa and Kaneko and Multiple Zeta Functions
We study for s ∈ N the functions ξk(s) = 1 Γ(s) R ∞ 0 t et−1 Lik(1−e )dt, and more generally ξk1,...,kr (s) = 1 Γ(s) R ∞ 0 t et−1 Lik1,...,kr (1 − e )dt, introduced by Arakawa and Kaneko [2] and relate them with (finite) multiple zeta functions, partially answering a question of [2]. In particular, we give an alternative proof of a result of Ohno [8].
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The Arakawa-Kaneko zeta functions interpolate the poly-Bernoulli numbers at the negative integers and their values at positive integers are connected to multiple zeta values. We give everywhere-convergent series expansions of these functions in terms of Bernoulli polynomials and Dirichlet series related to harmonic numbers, exhibiting their explicit analytic continuation. Differentiating the Ba...
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Throughout this paper Zp, Qp, C and Cp will respectively denote the ring of p-adic rational integers, the field of p-adic rational numbers, the complex number field and the completion of algebraic closure of Qp. The p-adic absolute value in Cp is normalized so that |p|p = 1 p . When one talks of q-extension, q is variously considered as an indeterminate, a complex number q ∈ C or a p-adic numbe...
متن کاملEuler Numbers and Polynomials Associated with Zeta Functions
Throughout this paper Z, Q, C, Zp, Qp and Cp will respectively denote the ring of rational integers, the field of rational numbers, the filed of complex numbers, the ring p-adic rational integers, the field of p-adic rational numbers, and the completion of the algebraic closure of Qp. Let vp be the normalized exponential valuation of Cp such that |p|p = p −vp(p) = p. If q ∈ Cp, we normally assu...
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ژورنال
عنوان ژورنال: Functiones et Approximatio Commentarii Mathematici
سال: 2014
ISSN: 0208-6573
DOI: 10.7169/facm/2014.51.1.1