• Journal of Applied and Pure Mathematics
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• v.4 no.5_6
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• pp.221-231
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• 2022

In this paper, we study differential equations arising from the generating functions of (p, q)-Hermite polynomials. We use this differential equation to give explicit identities for (p, q)-Hermite polynomials.

• 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.

• Honam Mathematical Journal
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• v.33 no.2
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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.

• Journal of applied mathematics & informatics
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• v.42 no.2
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• pp.457-469
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• 2024

In this paper, we construct higher-order (p, q)-poly-tangent numbers and polynomials and give several properties, including addition formula and multiplication formula. Finally, we explore the distribution of roots of higher-order (p, q)-poly-tangent polynomials.

• Kyungpook Mathematical Journal
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• v.54 no.1
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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.

• Journal of applied mathematics & informatics
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• v.41 no.4
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• pp.753-763
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• 2023

In this paper, we introduce a fully modified (p, q)-poly tangent polynomials and numbers of the first type. We investigate analytic properties that is related with (p, q)-Gaussian binomial coefficients. We also define (p, q)-Stirling numbers of the second kind and fully modified (p, q)-poly tangent polynomials and numbers of the first type with two variables. Moreover, we derive some identities are concerned with the modified tangent polynomials and the (p, q)-Stirling numbers.

• Honam Mathematical Journal
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• v.34 no.1
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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.

• Communications of the Korean Mathematical Society
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• v.28 no.3
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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.

• Journal of applied mathematics & informatics
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• v.30 no.1_2
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• pp.321-325
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• 2012

In this paper, we consider twisted $q$-Euler polynomials and define a $p$-adic $q$-transfer operator (see [6]). From this operator, we investigate the eigenvalues of the $p$-adic $q$-transfer operator on the space of twisted $q$-Euler polynomials.

• Journal of the Korean Mathematical Society
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• v.56 no.1
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• pp.265-284
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• 2019

The main purpose of this paper is to investigate the q-Apostol type Frobenius-Euler numbers and polynomials. By using generating functions for these numbers and polynomials, we derive some alternative summation formulas including powers of consecutive q-integers. By using infinite series representation for q-Apostol type Frobenius-Euler numbers and polynomials including their interpolation functions, we not only give some identities and relations for these numbers and polynomials, but also define generating functions for new numbers and polynomials. Further we give remarks and observations on generating functions for these new numbers and polynomials. By using these generating functions, we derive recurrence relations and finite sums related to these numbers and polynomials. Moreover, by applying higher-order derivative to these generating functions, we derive some new formulas including the Hurwitz-Lerch zeta function, the Apostol-Bernoulli numbers and the Apostol-Euler numbers. Finally, for an application of the generating functions, we derive a multiplication formula, which is very important property in the theories of normalized polynomials and Dedekind type sums.