• Kyungpook Mathematical Journal
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• 제54권1호
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• pp.131-141
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• 2014

In the present paper, we introduce the new generalization of q-Genocchi polynomials and numbers of higher order. Also, we give some interesting identities. Finally, by applying q-Mellin transformation to the generating function for q-Genocchi polynomials of higher order put we define novel q-Hurwitz-Zeta type function which is an interpolation for this polynomials at negative integers.

• 호남수학학술지
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• 제33권2호
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• pp.173-179
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• 2011

The main aim of this paper is to give some relationships between q-Bernstein, higher order genocchi and Euler polynomials.

• 대한수학회논문집
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• 제33권2호
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• pp.619-630
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• 2018

In this paper, we obtain a (p, q)-extension of the Whittaker function $M_{k,{\mu}}(z)$ together with its integral representations, by using the extended confluent hypergeometric function of the first kind ${\Phi}_{p,q}(b;c;z)$ [recently extended by J. Choi]. Also, we give some of its main properties, namely the summation formula, a transformation formula, a Mellin transform, a differential formula and inequalities. In addition, our extension on Whittaker function finds interesting connection with the Laguerre 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.