Multi-poly-Bernoulli numbers and related zeta functions

M Kaneko, H Tsumura - Nagoya Mathematical Journal, 2018 - cambridge.org
We construct and study a certain zeta function which interpolates multi-poly-Bernoulli
numbers at nonpositive integers and whose values at positive integers are linear …

Poly-Euler polynomials and Arakawa--Kaneko type zeta functions

Y Hamahata - Functiones et Approximatio Commentarii …, 2014 - projecteuclid.org
POLY-EULER POLYNOMIALS AND ARAKAWA–KANEKO TYPE ZETA FUNCTIONS
Yoshinori Hamahata 1. Introduction Euler polynomials En(x) (n = Page 1 Functiones et …

Poly-Cauchy numbers with a q parameter

T Komatsu - The Ramanujan Journal, 2013 - Springer
The concept of poly-Cauchy numbers was recently introduced by the author. The poly-
Cauchy number is a generalization of the Cauchy number just as the poly-Bernoulli number …

Incomplete poly-Bernoulli numbers associated with incomplete Stirling numbers

T Komatsu, K Liptai, I Mező - arXiv preprint arXiv:1510.05799, 2015 - arxiv.org
By using the associated and restricted Stirling numbers of the second kind, we give some
generalizations of the poly-Bernoulli numbers. We also study their arithmetical and …

On generalized poly-Bernoulli numbers and related L-functions

Y Sasaki - Journal of Number Theory, 2012 - Elsevier
Different two generalizations of the Dirichlet L-functions which are based on the construction
of Arakawa–Kanekoʼs zeta function are treated. Further special values at non-positive …

[HTML][HTML] Inverse binomial series and values of Arakawa–Kaneko zeta functions

MA Coppo, B Candelpergher - Journal of Number Theory, 2015 - Elsevier
In this article, we present a variety of evaluations of series of polylogarithmic nature. More
precisely, we express the special values at positive integers of two classes of zeta functions …

Incomplete poly-Cauchy numbers

T Komatsu - Monatshefte für Mathematik, 2016 - Springer
By using the restricted and associated Stirling numbers of the first kind by generalizing the
(unsigned) Stirling numbers of the first kind, we define the incomplete poly-Cauchy numbers …

More properties on multi-poly-Euler polynomials

H Jolany, RB Corcino, T Komatsu - Boletín de la Sociedad Matemática …, 2015 - Springer
In this paper, we establish more properties of generalized poly-Euler polynomials with three
parameters and we investigate a kind of symmetrized generalization of poly-Euler …

Explicit formula for generalization of Poly-Bernoulli numbers and polynomials with a, b, c parameters

H Jolany, RB Corcino - arXiv preprint arXiv:1109.1387, 2011 - arxiv.org
In this paper we investigate special generalized Bernoulli polynomials with a, b, c
parameters that generalize classical Bernoulli numbers and polynomials. The present paper …

Explicit relations between multiple zeta values and related variants

C Xu - Advances in Applied Mathematics, 2021 - Elsevier
In this paper we present some new identities for multiple polylogarithms (abbr. MPLs) and
multiple harmonic star sums (abbr. MHSSs) by using the methods of iterated integral …