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Related papers: Degenerate Euler zeta function

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Special functions like the polygamma, Hurwitz zeta, and Lerch zeta functions have sporadically been connected with the nth derivatives of trigonometric functions. We show the polylogarithm $\text{Li}_s(z)$, a function of complex argument…

General Mathematics · Mathematics 2024-05-31 Andrew Ducharme

In this paper, we consider degenerate Carlitz's type q-Euler polynmials and numbers and we investigate some identities arising from the fermionic p-adic integral equations and the generating function of thoe polynomials.

Number Theory · Mathematics 2015-07-17 Dmitry V. Dolgy , Taekyun Kim , Jin-Woo Park , Jong-Jin Seo

This study deals with certain harmonic zeta functions, one of them occurs in the study of the multiplication property of the harmonic Hurwitz zeta function. The values at the negative even integers are found and Laurent expansions at poles…

Number Theory · Mathematics 2024-03-13 Mümün Can , Levent Kargın , Mehmet Cenkci , Ayhan Dil

We introduce degenerate Hermite polynomials as a degenerate version of the ordinary Hermite polynomials. Then, among other things, by using the formula about representing one lambda-Sheffer polynomial in terms of other lambda-Sheffer…

Number Theory · Mathematics 2020-10-29 Taekyun Kim , Dae San Kim , Lee-Chae Jang , Hyunseok Lee , Hanyoung Kim

This paper continues a series of investigations on converging representations for the Riemann Zeta function. We generalize some identities which involve Riemann's zeta function, and moreover we give new series and integrals for the zeta…

Number Theory · Mathematics 2012-02-01 Alois Pichler

The degeneration of the hyperelliptic sigma function is studied. We use the Sato Grassmannian for this purpose. A simple decomposition of a rational function gives a decomposition of Pl\"ucker coordinates of a frame of the Sato…

Exactly Solvable and Integrable Systems · Physics 2020-03-06 Julia Bernatska , Victor Enolski , Atsushi Nakayashiki

In a previous paper, Rahmani introduced a new family of p-Bernoulli numbers and polynomials by means of the Gauss hypergeometric function. Motivated by this paper and as a degenerate version of those numbers and polynomials, we introduce…

Number Theory · Mathematics 2021-01-07 Taekyun Kim , Dae san Kim , Lee-Chae jang , Hyunseok Lee , Hanyoung Kim

In this paper we derive two expressions for the Hurwitz zeta function involving the complete Bell polynomials in the restricted case where q is a positive integer greater than 1. The arguments of the complete Bell polynomials comprise the…

Classical Analysis and ODEs · Mathematics 2008-03-11 Donal F. Connon

In this work, we consider the generating function of Kim's q-Euler polynomials and introduce new generalization of q-Genocchi polynomials and numbers of higher order. Also, we give surprising identities for studying in Analytic Numbers…

Number Theory · Mathematics 2019-07-04 Serkan Araci , Mehmet Acikgoz , Jong Jin Seo

We present a remarkably simple and surprisingly natural interpretation of the values of zeta functions at negative integers and zero. Namely we are able to relate these values to areas related to partial sums of powers. We apply these…

Number Theory · Mathematics 2022-09-12 Ján Mináč , Nguyen Duy Tân , Nguyen Tho Tung

Maximon has recently given an excellent summary of the properties of the Euler dilogarithm function and the frequently used generalizations of the dilogarithm, the most important among them being the polylogarithm function $Li_(z)$. The…

Classical Analysis and ODEs · Mathematics 2009-11-24 Djurdje Cvijović

For the Tornheim double zeta function T(s1,s2,s3) of complex variables,we obtain its functional equations,which are new.Using the calculus of r-th order derivative of zeta(s,alpha) as a function of alpha(developed in author[7])as the…

Number Theory · Mathematics 2011-08-17 Vivek V. Rane

We introduce and study subalgebra cotype zeta functions, multivariate zeta functions enumerating fixed-index subalgebras of $R$-algebras of a given cotype. This generalizes and unifies previous works on subalgebra zeta functions and cotype…

Rings and Algebras · Mathematics 2025-09-25 Seok Hyeong Lee , Seungjai Lee

The aim of this paper is to further study some properties and identities on the degenerate Fubini and the degenerate Bell polynomials which are degenerate versions of the Fubini and the Bell polynomials, respectively. Especially, we find…

Number Theory · Mathematics 2022-03-02 Taekyun Kim , Dae san Kim

Pellarin introduced the deformation of multiple zeta values of Thakur as elements over Tate algebras. In this paper, we relate these values to a certain coordinate of a higher dimensional Drinfeld module over Tate algebras which we will…

Number Theory · Mathematics 2021-08-24 Oğuz Gezmiş

The local topological zeta function is a rational function associated to a germ of a complex holomorphic function. This function can be computed from an embedded resolution of singularities of the germ. For nondegenerate functions it is…

Algebraic Geometry · Mathematics 2008-05-14 Ann Lemahieu , Lise Van Proeyen

It was observed by Bump et al. that Ehrhart polynomials in a special family exhibit properties similar to the Riemann {\zeta} function. The construction was generalized by Matsui et al. to a larger family of reflexive polytopes coming from…

Combinatorics · Mathematics 2018-04-20 Akihiro Higashitani , Mario Kummer , Mateusz Michałek

A generalization of Arnold's strange duality to invertible polynomials in three variables by the first author and A.Takahashi includes the following relation. For some invertible polynomials $f$ the Saito dual of the reduced monodromy zeta…

Algebraic Geometry · Mathematics 2010-09-09 Wolfgang Ebeling , Sabir M. Gusein-Zade

In this paper, we investigate the properties of symmetry in two variables related to multiple Euler q-l-function which interpolates higher-order q-Euler polynomials at negative integers. From our investigation, we can derive many…

Number Theory · Mathematics 2013-12-18 D. V. Dolgy , D. S. Kim , T. G. Kim , J. J. Seo

We give an explicit formula of the coefficients of the Zeta-Function's L-polynomial for algebraic function fields over finite constant fields. Thus, we deduce an expression of the class number of algebraic function fields defined over…

Algebraic Geometry · Mathematics 2026-02-26 Mahdi Mohamed Koutchoukali