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We give some new identities for (h; q)-Genocchi numbers and polynomials by means of the fermionic p-adic q-integral on Zp and the weighted q-Bernstein polynomials.

Number Theory · Mathematics 2019-07-04 Serkan Araci , Elif Cetin , Mehmet Acikgoz , Ismail Naci Cangul

In this paper, we derive eight basic identities of symmetry in three variables related to $q$-Bernoulli polynomials and the $q$-analogue of power sums. These and most of their corollaries are new, since there have been results only about…

Number Theory · Mathematics 2010-03-18 Dae San Kim

We give "hybrid" proofs of the $q$-binomial theorem and other identities. The proofs are "hybrid" in the sense that we use partition arguments to prove a restricted version of the theorem, and then use analytic methods (in the form of the…

Number Theory · Mathematics 2019-01-17 Dennis Eichhorn , James Mc Laughlin , Andrew V. Sills

We derive some q-analogs of Euler-Cassini-type identities and of recurrence formulas for powers of Fibonacci polynomials.

Combinatorics · Mathematics 2008-06-11 Johann Cigler

We present outlines of a general method to reach certain kinds of $q$-multiple sum identities. Throughout our exposition, we shall give generalizations to the results given by Dilcher, Prodinger, Fu and Lascoux, Zeng, and Guo and Zhang…

Combinatorics · Mathematics 2025-06-09 Aung Phone Maw

The purpose of this paper is to give symmetric identities for higher-order degenerate q- Bernoulli polynomials arising from the p-adic q-integral on Zp.

Number Theory · Mathematics 2016-08-18 Taekyun Kim , Hyuck-In Kwon

By applying the derivative operator to the corresponding hypergeometric form of a $q$-series transformation due to Andrews [1,Theorem 4], we establish a general harmonic number identity. As the special cases of it, several interesting…

Combinatorics · Mathematics 2011-11-15 Chuanan Wei , Dianxuan Gong

We present several identities with a form of polynomials or rational functions that involve Pochhammer and q-Pochhammer symbols and q-binomials (i.e. Gauss polynomials). All these identities were obtained by some analytical methods based on…

Analysis of PDEs · Mathematics 2025-05-02 Paweł J. Szabłowski

In this paper, we give some new and interesting identities which are derived from the basis of Frobenius-Euler. Recently, Simsek et als(see [13]) have given some identities of q-analogue of Frobenius-Euler polynomials related to q-Bernstein…

Number Theory · Mathematics 2012-11-29 Dae San Kim , Taekyun Kim

We construct the q-analogue of Euler-Barnes' numbers and polynomials, and investigate their some properties.

Number Theory · Mathematics 2007-05-23 Taekyun Kim , Lee-Chae Jang

In this paper, we investigate some symmetric properties of the multivariate p-adic fermionic integrals on Zp and derive various identities concerning the expansions of q-Euler polynomials from the symmetric properties of the multivariate…

Number Theory · Mathematics 2014-01-15 Dae San Kim , Tae Gyun Kim

We describe a bilinear identity satisfied by certain multidimensional q-hypergeometric integrals. The identity can be considered as a deformation of the Riemann bilinear relation for the twisted de Rham (co)homologies. The identity also…

q-alg · Mathematics 2008-02-03 Vitaly Tarasov

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 give a convolution identity for the complete and elementary symmetric functions. This result can be used to proving and discovering some combinatorial identities involving $r$-Stirling numbers, $r$-Whitney numbers and…

Number Theory · Mathematics 2018-11-13 Mircea Merca

The $q$-binomial coefficients are q-analogues of the binomial coefficients, counting the number of $k$-dimensional subspaces in the $n$-dimensional vector space $\mathbb{F}^n_q$ over $\mathbb{F}_{q}$. In this paper, we define a Euclidean…

Combinatorics · Mathematics 2023-08-31 Semin Yoo

Recently, Kim-Jang-Yi have introduced q-Bernstein polynomials. From these q-Berstein polynomials, we investigte some properties related to q-Stirling numbes and q-Bernoulli numbes.

Number Theory · Mathematics 2010-06-11 Taekyun Kim , Jongsung Choi , Young-Hee Kim

We state and prove a number of unilateral and bilateral $q$-series identities and explore some of their consequences. Those include certain generalizations of the $q$-binomial sum which also generalize the $q$-Airy function introduced by…

Classical Analysis and ODEs · Mathematics 2016-02-02 Ahmad El-Guindy , Mourad E. H. Ismail

In recent years, there has been intensive research on the ${\mathbb Q}$-linear relations between multiple zeta (star) values. In this paper, we prove many families of identities involving the $q$-analog of these values, from which we can…

Number Theory · Mathematics 2018-06-26 Khodabakhsh Hessami Pilehrood , Tatiana Hessami Pilehrood , Jianqiang Zhao

In the present article, we introduce a $(p,q)$-analogue of the poly-Euler polynomials and numbers by using the $(p,q)$-polylogarithm function. These new sequences are generalizations of the poly-Euler numbers and polynomials. We give…

Number Theory · Mathematics 2016-04-14 Takao Komatsu , José L. Ramírez , Víctor F. Sirvent

In this paper, by the technique of inverse relations and comparing coefficients, we establish some generalized forms of Andrews' q-series identity and two new Bailey pairs and q-identities closely related to Andrews-Warnaar's sum identity…

Combinatorics · Mathematics 2026-03-31 Qi Chen