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In this paper, we give some new identities of symmetry for q-Bernoulli polynomials under the symmetric group of degree n arising from p-adic q-integrals on Zp.

Number Theory · Mathematics 2015-04-22 Dae san Kim , Taekyun Kim

By the symmetric properties of Drichlet's type multiple q-l-function, we establish various identities concerning the generalized higher-order q-Euler polynomials. Furthermore, we give some interesting relationship between the power sums and…

Number Theory · Mathematics 2013-12-31 Dae San Kim , Taekyun Kim

In this paper, we continue our investigation of double sums where the inner sum is binomial but incomplete. We prove many new results for these types of double sums associated with binomial transform pairs. As applications we deduce new…

Combinatorics · Mathematics 2025-11-20 Kunle Adegoke , Robert Frontczak , Karol Gryszka

In this paper we use probabilistic methods to derive some results on the generalized Bernoulli and generalized Euler polynomials. Our approach is based on the properties of Appell polynomials associated with uniformly distributed and…

Probability · Mathematics 2013-07-18 Bao Quoc Ta

In this paper, we consider the poly-Bernoulli numbers and polynomials of the second kind and presents new and explicit formulae for calculating the poly-Bernoulli numbers of the second kind and the Stirling numbers of the second kind.

Number Theory · Mathematics 2014-06-25 Taekyun Kim , Sang-Hun Lee , Jongjin Seo

We obtain closed form expressions for convolutions of scale transformations within a certain subset of Appell polynomials. This subset contains the Bernoulli, Apostol-Euler, and Cauchy polynomials, as well as various kinds of their…

Number Theory · Mathematics 2018-05-14 José A. Adell , Alberto Lekuona

The purpose of this paper is to derive some identities of the higher order generalized twisted Bernoulli numbers and polynomials attached to $\chi$ from the properties of the p-adic invariant integrals.

Number Theory · Mathematics 2009-07-20 Younghee Kim , Seog-Hoon Rim , Byungje Lee , Taekyun Kim

A number of identities are proved by using Stirling transforms. These identities involve Stirling numbers of the first and second kinds, hyperharmonic and derangement numbers, Bernoulli and Euler numbers and polynomials, powers, power sums,…

Number Theory · Mathematics 2021-01-18 Khristo N. Boyadzhiev

In this paper we introduce a new sequence of polynomials, which follow the same recursive rule of the well-known Lucas-Lehmer integer sequence. We show the most important properties of this sequence, relating them to the Chebyshev…

Classical Analysis and ODEs · Mathematics 2017-03-07 Pierluigi Vellucci , Alberto Maria Bersani

We establish new connection formulae between Fibonacci polynomials and Chebyshev polynomials of the first and second kinds. These formulae are expressed in terms of certain values of hypergeometric functions of the type 2F1. Consequently,…

Number Theory · Mathematics 2017-01-19 W. M. Abd-Elhameed , Y. H. Youssri , N. El-Sissi , M. Sadek

A class P_{n,m,p}(x) of polynomials is defined. The combinatorial meaning of its coefficients is given. Chebyshev polynomials are the special cases of P_{n,m,p}(x). It is first shown that P_{n,m,p}(x) may be expressed in terms of…

Complex Variables · Mathematics 2008-04-15 Milan Janjic

Recently, Kim-Kim Introduced some interesting identities of symmetry for q-Bernoulli polynomials under symmetry group of degree n. In this paper, we study the degenerate q-Euler polynomials and derive some identities of symmetry for these…

Number Theory · Mathematics 2016-08-02 D. V. Dolgy , T. Kim , L. -C. Jang , H. -I Kwon

We prove that the Eulerian polynomial satisfies certain polynomial congruences. Furthermore, these congruences characterize the Eulerian polynomial.

Combinatorics · Mathematics 2021-09-03 Kazuki Iijima , Kyouhei Sasaki , Yuuki Takahashi , Masahiko Yoshinaga

In this paper, we consider the q-extensions of Boole polynomials. From those polynomials, we derive some new and interesting properties and identities related to special polynomials.

Number Theory · Mathematics 2014-03-19 Dae San Kim , Taekyun Kim , Jong Jin Seo

We are interested in irrationality of roots for seven important families of polynomials : Tchebichef polynomials, Legendre polynomials, Laguerre polynomials, Hermite polynomials, Bessel polynomials, Bernoulli polynomials and Euler…

Number Theory · Mathematics 2017-07-26 Lionel Ponton

We give a simple formula for some determinants, and an analogous formula for pfaffians, both of which are polynomial identities. The second involve some expressions that interpolate between determinants and pfaffians. We give several…

Combinatorics · Mathematics 2021-03-31 David Anderson , William Fulton

In this paper, we investigate some new symmetric identities for the q-Euler polynomials under the symmetric group of degree n which are derived from fermionic p-adic q-integrals on Zp.

Number Theory · Mathematics 2015-04-23 Dmitry V. Dolgy , Dae San Kim , Taekyun Kim

In this paper, we derive some interesting symmetric properties for the geenralized Euler numbers and polynomials.

Number Theory · Mathematics 2009-07-29 T. Kim

In this paper, we investigate some properties of several Sheffer sequences of several polynomials arising from umbral calculus. From our investigation, we can derive many interesting identities of several polynomials

Number Theory · Mathematics 2013-02-21 Taekyun Kim , Dae San Kim , Seog-Hoon Rim , Dmitry V. Dolgy

In this paper, we study some properties of associated sequences of special polynomials. From the properties of associated sequences of polynomials, we derive some interesting identities of special polynomials.

Number Theory · Mathematics 2013-01-23 Taekyun Kim , Dae San Kim