• Journal of applied mathematics & informatics
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• 제27권3_4호
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• pp.453-462
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• 2009

Kim [4] defined the generalized Genocchi numbers $G_{n,x}$. In this paper, we introduce the generalized Genocchi polynomials $G_{n,x}(x)$. One purpose of this paper is to investigate the zeros of the generalized Genocchi polynomials $G_{n,x}(x)$. We also display the shape of generalized Genocchi polynomials $G_{n,x}(x)$.

• 대한수학회지
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• 제43권1호
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• pp.183-198
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• 2006

In this paper q-extensions of Genocchi numbers are defined and several properties of these numbers are presented. Properties of q-Genocchi numbers and polynomials are used to construct q-extensions of p-adic measures which yield to obtain p-adic interpolation functions for q-Genocchi numbers. As an application, general systems of congruences, including Kummer-type congruences for q-Genocchi numbers are proved.

• Journal of applied mathematics & informatics
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• 제22권1_2호
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• pp.125-132
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• 2006

It is the aim of this paper to introduce the Genocchi numbers Gn and polynomials Gn(x) and to display the shape of Genocchi polynomials Gn(x). Finally, we investigate the roots of the Genocchi polynomials Gn(x).

• Journal of applied mathematics & informatics
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• 제32권3_4호
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• pp.465-474
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• 2014

Many mathematicians have studied various relations beween Euler number $E_n$, Bernoulli number $B_n$ and Genocchi number $G_n$ (see [1-18]). They have found numerous important applications in number theory. Howard, T.Agoh, S.-H.Rim have studied Genocchi numbers, Bernoulli numbers, Euler numbers and polynomials of these numbers [1,5,9,15]. T.Kim, M.Cenkci, C.S.Ryoo, L. Jang have studied the q-extension of Euler and Genocchi numbers and polynomials [6,8,10,11,14,17]. In this paper, our aim is introducing and investigating an extension term of generalized Euler polynomials. We also obtain some identities and relations involving the Euler numbers and the Euler polynomials, the Genocchi numbers and Genocchi polynomials.

• Journal of applied mathematics & informatics
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• 제30권1_2호
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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.

• 호남수학학술지
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• 제32권4호
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• pp.563-579
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• 2010

In this paper we introduce the new analogs of Genocchi numbers and polynomials. Finally, we investigate the zeros of the twisted (h,q)-extension of Genocchi polynomials ${G_{n,q,w}^{(h)}}$(x).

• 대한수학회논문집
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• 제28권3호
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• pp.457-462
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• 2013

In the present paper, we analyse analytic continuation of weighted $q$-Genocchi numbers and polynomials. A novel formula for weighted $q$-Genocchi-zeta function $\tilde{\zeta}_{G,q}(s{\mid}{\alpha})$ in terms of nested series of $\tilde{\zeta}_{G,q}(n{\mid}{\alpha})$ is derived. Moreover, we introduce a novel concept of dynamics of the zeros of analytically continued weighted $q$-Genocchi polynomials.

• 충청수학회지
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• 제26권1호
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• pp.231-242
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• 2013

In this work, we deal with $q$-Genocchi numbers and polynomials. We derive not only new but also interesting properties of the $q$-Genocchi numbers and polynomials. Also, we give Cauchy-type integral formula of the $q$-Genocchi polynomials and derive distribution formula for the $q$-Genocchi polynomials. In the final part, we introduce a definition of $q$-Zeta-type function which is interpolation function of the $q$-Genocchi polynomials at negative integers which we express in the present paper.

• 충청수학회지
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• 제24권4호
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• pp.905-918
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• 2011

The main properties of this paper is to describe the higher order q-Genocchi polynomials with weight $({\alpha},{\beta})$. However, we derive some interesting properties concerning this type of polynomials.

• 호남수학학술지
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• 제34권1호
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• pp.11-18
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• 2012

Recently, T. Kim has introduced and analysed the q-Bernoulli numbers and polynomials with weight ${\alpha}$ cf.[7]. By the same motivaton, we also give some interesting properties of the q-Genocchi numbers and polynomials with weight ${\alpha}$. Also, we derive the q-extensions of zeta type functions with weight from the Mellin transformation of this generating function which interpolates the q-Genocchi polynomials with weight at negative integers.