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In this paper, we derive eight basic identities of symmetry in three variables related to generalized Euler polynomials and alternating generalized power sums. All of these are new, since there have been results only about identities of…

Number Theory · Mathematics 2010-03-23 Dae San Kim

In this paper, we investigate new class of sequences related to fully degenerate Bernoulli numbers and polynomials. From those sequences, we derive some formulae for the degenerate Bernoulli and Euler polynomials.

Number Theory · Mathematics 2022-03-09 Taekyun Kim , Dae san Kim

In this paper, some formulae for Genoochi polynomials of higher order are derived using the fact that sets of Bernoulli and Euler polynomials of higher order form basis for the polynomial space.

Classical Analysis and ODEs · Mathematics 2020-09-09 Cristina B. Corcino , Roberto B. Corcino , Joy Ann A. Canete

In this paper, we study some symmetric identities of q-Euler numbers and polynomials. From these properties, we derive several identities of q-Euler numbers and polynomials.

Number Theory · Mathematics 2013-10-08 Dae San Kim , Taekyun Kim

We present an algebraic generalization of Euler's theorem for quadrilaterals. Starting from the parallelogram identity in an inner product space, we derive Apollonius' identity and obtain Euler's quadrilateral identity in a unified vector…

General Mathematics · Mathematics 2026-03-18 Mohammad Hassan Murad

In this paper we establish two symmetric identities on sums of products of Euler polynomials.

Combinatorics · Mathematics 2010-04-02 Yong Zhang , Zhi-Wei Sun , Hao Pan

In \cite{luo2006,luosri2005}, Luo and Srivastava introduced some generalizations of the Apostol -Bernoulli polynomials and the Apostol-Euler polynomials. The main object of this paper is to extend the result of \cite{prevost2010} to these…

Number Theory · Mathematics 2017-09-19 Marc Prévost

The purpose of this paper is to present a systemic study of some families of multiple q-Genocchi and euler numbers by using multivariate q-Volkenborn integral. From the studies of those q-Genocchi numbers and polynomials of higher order we…

Number Theory · Mathematics 2009-11-13 Taekyun Kim

In this paper, we provide some novel binomial convolution related to symmetric functions, as well as convolution sums without the binomial symbol. Moreover we give some new convolution sums of Bernoulli, Euler, and Genocchi numbers and…

Combinatorics · Mathematics 2025-04-30 Meryem Bouzeraib , Ali Boussayoud , Salah Boulaaras

In this paper, we mainly show that Euler sums of generalized hyperharmonic numbers can be expressed in terms of linear combinations of the classical Euler sums.

Number Theory · Mathematics 2021-03-22 Rusen Li

The aim of this paper is to study degenerate Eulerian polynomials and degenerate Eulerian numbers, respectively as degenerate versions of the Eulerian polynomials and the Eulerian numbers, and to derive some of their properties.…

Number Theory · Mathematics 2024-12-05 Taekyun Kim , Dae san Kim

This paper introduces a degenerate version of the Euler-Seidel method by incorporating a parameter lambda into the classical recurrence relation. We define a degenerate Euler-Seidel matrix associated with an initial sequence and establish…

Number Theory · Mathematics 2025-12-24 Taekyun Kim , Dae San Kim , Hyunseok Lee , Kyo-Shin Hwang

We define a truncated Euler polynomial $E_{m,n}(x)$ as a generalization of the classical Euler polynomial $E_n(x)$. In this paper we give its some properties and relations with the hypergeometric Bernoulli polynomial.

Number Theory · Mathematics 2018-02-22 Takao Komatsu , Claudio de J. Pita Ruiz

We present a relationship between the generalized hyperharmonic numbers and the poly-Bernoulli polynomials, motivated from the connections between harmonic and Bernoulli numbers. This relationship yields numerous identities for the…

Number Theory · Mathematics 2021-05-11 Levent Kargın , Mehmet Cenkci , Ayhan Dil , Mümün Can

The Concepts of poly-Bernoulli numbers $B_n^{(k)}$, poly-Bernoulli polynomials $B_n^{k}{(t)}$ and the generalized poly-bernoulli numbers $B_{n}^{(k)}(a,b)$ are generalized to $B_{n}^{(k)}(t,a,b,c)$ which is called the generalized…

Number Theory · Mathematics 2012-12-18 Hassan Jolany , M. R. Darafsheh , R. Eizadi Alikelaye

For the Schur polynomials bounded and unbounded generalizations of the Cauchy identities are found.

Combinatorics · Mathematics 2026-01-27 Leonid Bedratyuk

The main purpose of this paper is to introduce and investigate a class of $q$-Bernoulli, $q$-Euler and $q$-Genocchi polynomials. The $q$-analogues of well-known formulas are derived. The $q$-analogue of the Srivastava--Pint\'er addition…

Classical Analysis and ODEs · Mathematics 2014-01-21 N. I. Mahmudov , M. Momenzadeh

Thw purpose of this paper is to present a systemic study of some families of the generalized q-Euler numbers and polynomials of higher order.

Number Theory · Mathematics 2009-12-25 Taekyun Kim

We lift to the multivariate Eulerian polynomials the identity implying that univariate Eulerian polynomials are palindromic. As a consequence of this generalization, we obtain nice combinatorial identities that can be directly extracted…

Combinatorics · Mathematics 2026-01-23 Alejandro González Nevado

In this paper, we derive some new and interesting idebtities for Bernoulli, Euler and Hermite polynomials associated with Chebyshev polynomials.

Number Theory · Mathematics 2012-11-08 Dae San Kim , Taekyun Kim , Sang-Hun Lee