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Related papers: On multi-poly-Bernoulli-Carlitz numbers

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In this paper, we consider Hermite and poly-Bernoulli mixed-type polynomials and investigate the properties of those polynomials which are derived from umbral calculus. Finally, we give various identities associated with Stirling numbers,…

Number Theory · Mathematics 2013-10-07 Dae san Kim , taekyun Kim

This paper is devoted to establishing several new formulas relating Bernoulli and Stirling numbers of both kinds.

Number Theory · Mathematics 2024-12-24 Bakir Farhi

In this paper, we establish some new identities of integrals involving multiple polylogarithm functions and their level two analogues in terms of Hurwitz-type multiple zeta (star) values. Using these identities, we provide new proofs of the…

Number Theory · Mathematics 2025-01-22 Masanobu Kaneko , Weiping Wang , Ce Xu , Jianqiang Zhao

The aim of this paper is to give a new approach to modified q-Bernstein polynomials for functions of two variables. By using these type polynomials, we derive recurrence formulas and some new interesting identities related to the second…

Number Theory · Mathematics 2013-12-06 Mehmet Acikgoz , Serkan Araci

We give an instant evaluation of multiple Zeta function at non-positive integers by elementary methods and discuss the Fourier theory (on unit interval) of the product of Bernoulli polynomials.We also show that the polynomial expression for…

Number Theory · Mathematics 2009-11-10 Vivek V. Rane

In this paper, we introduce the concept of the (higher order) Appell-Carlitz numbers which unifies the definitions of several special numbers in positive characteristic, such as the Bernoulli-Carlitz numbers and the Cauchy-Carlitz…

Number Theory · Mathematics 2021-09-06 Su Hu , Min-Soo Kim

We introduce the $B$-Stirling numbers of the first and second kind, which are the coefficients of the potential polynomials when we express them in terms of the monomials and the falling factorials, respectively. These numbers include, as…

Combinatorics · Mathematics 2024-10-17 José A. Adell , Beáta Bényi

In the paper, the authors establish an explicit formula for computing Bernoulli polynomials at non-negative integer points in terms of $r$-Stirling numbers of the second kind.

Combinatorics · Mathematics 2017-06-08 Bai-Ni Guo , István Mező , Feng Qi

T. Ito defined an analog of the Arakawa-Kaneko zeta function to obtain relations among Mordell-Tornheim multiple zeta values. In this paper, we develop two things related to an analog of the Arakawa-Kaneko zeta function. One is to find an…

Number Theory · Mathematics 2018-04-02 Ryota Umezawa

Poly-Bernoulli numbers are one of generalizations of the classical Bernoulli numbers. Since a negative index poly-Bernoulli number is an integer, it is an interesting problem to study this number from combinatorial viewpoint. In this short…

Number Theory · Mathematics 2020-03-30 Toshiki Matsusaka

We prove nonlinear relation on multiple Hurwitz-Riemann zeta functions. Using analytic continuation of these multiple Hurwitz-Riemann zeta function, we quote at negative integers Euler's nonlinear relation for generalized Bernoulli…

Number Theory · Mathematics 2016-03-15 Abdelmejid Bayad , Takao Komatsu

Observing a multiple version of the divisor function we introduce a new zeta function which we call a multiple finite Riemann zeta function. We utilize some $q$-series identity for proving the zeta function has an Euler product and then,…

Number Theory · Mathematics 2015-06-26 K. Kimoto , N. Kurokawa , S. Matsumoto , M. Wakayama

Recently (see [1]) I has introduced an interesting the Euler-Barnes multiple zeta function. In this paper we construct the q-analogue of Euler-Barnes multiple zeta function which interpolates the q-analogue of Frobenius-Euler numbers of…

Number Theory · Mathematics 2007-05-23 Taekyun Kim

In this paper, we introduce the concepts of the $u$-bracket, finite multiple harmonic $u$-series, and $u$-multiple zeta values via the Carlitz module. These objects serve as function field counterparts to the classical theory of…

Number Theory · Mathematics 2026-04-07 Hung-Chun Tsui

We present several formulas for some specific multiple $L$-values of conductor four. This grew out from the study of zeta functions of level four of Arakawa-Kaneko type. Closely related is a new version of multiple poly-Euler numbers and we…

Number Theory · Mathematics 2022-08-11 Masanobu Kaneko , Hirofumi Tsumura

Various new identities, recurrence relations, integral representations, connection and explicit formulas are established for the Bernoulli, Euler numbers and the values of Riemann's zeta function. To do this, we explore properties of some…

Classical Analysis and ODEs · Mathematics 2014-06-23 Semyon Yakubovich

We find a representation for the Maclaurin coefficients of the Hurwitz zeta-function in terms of semi-convergent series involving the Bernoulli polynomials and the Stirling numbers of the first kind. In particular, this gives a…

Number Theory · Mathematics 2008-12-09 Khristo Boyadzhiev

I recent years, many mathematicians studied various degenerate version of some spcial polynomials of which quite a few interesting results were discovered. In this paper, we introduce the type 2 degenerate Bernoulli polynomials of the…

Number Theory · Mathematics 2019-08-20 Taekyun Kim , Lee-Chae jang , Dae San Kim , Han-Young Kim

In this paper, we consider the degenerate Carlitz q-Bernoulli numbers and polynomials and we investigate some properties of those polynomials.

Number Theory · Mathematics 2015-07-20 Taekyun Kim

We study a polynomial interpolation of finite multiple zeta and zeta-star values with variable $t$, which is an analogue of interpolated multiple zeta values introduced by Yamamoto. We introduce several relations among them and, in…

Number Theory · Mathematics 2020-08-25 Hideki Murahara , Masataka Ono