• Bulletin of the Korean Mathematical Society
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• v.50 no.2
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• pp.659-665
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• 2013

In this note, the $q$-extension of the twisted Lerch Euler zeta functions considered by Jang [Bull. Korean Math. Soc. 47 (2010), no. 6, 1181-1188] is further investigated, and the generalized multiplication theorem for the $q$-extension of the twisted Lerch Euler zeta functions is given. As applications, some well-known results in the references are deduced as special cases.

• Honam Mathematical Journal
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• v.36 no.3
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• pp.647-657
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• 2014

In this paper, we study combinatoric convolution sums of divisor functions and get values of this sum when $n=2^mp$. We find that the value of this convolution sum is represented by a sum of powers of 2 and Bernoulli or Euler number.

• Journal of applied mathematics & informatics
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• v.30 no.1_2
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• pp.337-346
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• 2012

In this paper we construct a new type of twisted $q$-Genocchi numbers $G_{n,q,w}^{({\alpha})}$ and polynomials $G_{n,q,w}^{({\alpha})}(x)$. Some interesting results and relationships are obtained.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.9 no.2
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• pp.1-15
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• 2005

In this article, a generalisation of Sard's inequality for Appell polynomials is obtained. Estimates for the remainder are also provided.

• Bulletin of the Korean Mathematical Society
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• v.50 no.4
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• pp.1289-1296
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• 2013

Recently, T. Kim has introduced and analysed the $q$-Euler polynomials (see [3, 14, 35, 37]). By the same motivation, we will consider some interesting properties of the $q$-Genocchi polynomials. Further, we give some formulae on the Bernstein and $q$-Genocchi polynomials by using $p$-adic integral on $\mathbb{Z}_p$. From these relationships, we establish some interesting identities.

• Bulletin of the Korean Mathematical Society
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• v.43 no.3
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• pp.611-617
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• 2006

In this paper we construct q-Genocchi numbers and polynomials. By using these numbers and polynomials, we investigate the q-analogue of alternating sums of powers of consecutive integers due to Euler.

• Communications of the Korean Mathematical Society
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• v.35 no.2
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• pp.417-445
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• 2020

The purpose of this article is to continue the study of q, 𝜔-special functions in the spirit of Wolfgang Hahn from the previous papers by Annaby et al. and Varma et al., with emphasis on q, 𝜔-Apostol Bernoulli and Euler polynomials, Ward-𝜔 numbers and multiple q, 𝜔power sums. Like before, the q, 𝜔-module for the alphabet of q, 𝜔-real numbers plays a crucial role, as well as the q, 𝜔-rational numbers and the Ward-𝜔 numbers. There are many more formulas of this type, and the deep symmetric structure of these formulas is described in detail.

• Honam Mathematical Journal
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• v.34 no.3
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• pp.311-326
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• 2012

The purpose of this paper is to introduce and investigate two new classes of generalized Bernoulli and Apostol-Bernoulli polynomials based on the definition given recently by the authors [29]. In particular, we obtain a new addition formula for the new class of the generalized Bernoulli polynomials. We also give an extension and some analogues of the Srivastava-Pint$\acute{e}$r addition theorem [28] for both classes. Finally, by making use of the new adition formula, we exhibit several interesting relationships between generalized Bernoulli polynomials and other polynomials or special functions.

• Kyungpook Mathematical Journal
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• v.55 no.1
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• pp.29-39
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• 2015

In this paper, we investigate the functional equations of the multiple Dirichlet and Hurwitz L-functions associated with Bernoulli numbers and polynomials attached to Dirichlet character.

• East Asian mathematical journal
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• v.12 no.2
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• pp.183-190
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• 1996