• Journal of Applied and Pure Mathematics
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• v.5 no.3_4
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• pp.197-209
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• 2023

In this paper, the generalized (p, q)-poly-Genocchi polynomials with variable a is defined by generalizing it more, and various properties of this polynomial are introduced. To do this, we define a generating function and use the definition to introduce some interesting properties as follows: basic properties, relation between Stirling numbers of the second kind and generalized (p, q)-poly-Genocchi polynomials with variable a and symmetric properties.

• Journal of applied mathematics & informatics
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• v.28 no.3_4
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• pp.805-811
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• 2010

It is the aim of this paper to observe an interesting phenomenon of 'scattering' of the zeros of the q-Bernoulli polynomials $B_{n,q}(x)$ for -1 < q < 0 in complex plane. Observe that the structure of the zeros of the Genocchi polynomials $G_n(x)$ resembles the structure of the zeros of the q-Bernoulli polynomials $B_{n,q}(x)$ as q $\rightarrow$ -1.

• Journal of applied mathematics & informatics
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• v.28 no.5_6
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• pp.1277-1284
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• 2010

One purpose of this paper is to consider the reflection symmetries of the q-Genocchi polynomials $G^*_{n,q}(x)$. We also observe the structure of the roots of q-Genocchi polynomials, $G^*_{n,q}(x)$, using numerical investigation. By numerical experiments, we demonstrate a remarkably regular structure of the real roots of $G^*_{n,q}(x)$.

• Communications of the Korean Mathematical Society
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• v.36 no.3
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• pp.423-445
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• 2021

In this paper, a new form of poly-Genocchi polynomials is defined by means of polylogarithm, namely, the Apostol-type poly-Genocchi polynomials of higher order with parameters a, b and c. Several properties of these polynomials are established including some recurrence relations and explicit formulas, which are used to express these higher order Apostol-type poly-Genocchi polynomials in terms of Stirling numbers of the second kind, Apostol-type Bernoulli and Frobenius polynomials of higher order. Moreover, certain differential identity is obtained that leads this new form of poly-Genocchi polynomials to be classified as Appell polynomials and, consequently, draw more properties using some theorems on Appell polynomials. Furthermore, a symmetrized generalization of this new form of poly-Genocchi polynomials that possesses a double generating function is introduced. Finally, the type 2 Apostolpoly-Genocchi polynomials with parameters a, b and c are defined using the concept of polyexponential function and several identities are derived, two of which show the connections of these polynomials with Stirling numbers of the first kind and the type 2 Apostol-type poly-Bernoulli polynomials.

• Journal of applied mathematics & informatics
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• v.40 no.1_2
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• pp.233-242
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• 2022

The purpose of this paper is to find some properties and identities for (p, q)-cosine Genocchi polynomials. This polynomials which is one of Appell polynomials, have multifarious relations of (p, q)-other polynomials.

• Bulletin of the Korean Mathematical Society
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• v.50 no.2
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• pp.583-588
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• 2013

In this paper, we introduce the $q$-analogue of $p$-adic log gamma functions with weight alpha. Moreover, we give a relationship between weighted $p$-adic $q$-log gamma functions and $q$-extension of Genocchi and Euler numbers with weight alpha.

• Journal of applied mathematics & informatics
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• v.29 no.5_6
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• pp.1221-1228
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• 2011

Recently, several mathematicians have studied some interesting relations between extended q-Euler number and Bernstein polynomials(see [3, 5, 7, 8, 10]). In this paper, we give some interesting identities on the Genocchi polynomials and Bernstein polynomials.

• Honam Mathematical Journal
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• v.46 no.2
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• pp.168-180
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• 2024

The main object of this article is to propose a unified extension of Bernoulli, Euler and Genocchi polynomials by means of a new family of mixed polynomials whose generating function is given in terms of generalized Bessel function. We also discuss here some fundamental properties of our introduced mixed polynomials by making use of the series arrangement technique. Furthermore, some conclusions of our present study are also pointed out in the last section.

• Journal of the Korean Mathematical Society
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• v.55 no.5
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• pp.1179-1192
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• 2018

Several addition formulas for a general class of q-Appell sequences are proved. The q-addition formulas, which are derived, involved not only the generalized q-Bernoulli, the generalized q-Euler and the generalized q-Genocchi polynomials, but also the q-Stirling numbers of the second kind and several general families of hypergeometric polynomials. Some q-umbral calculus generalizations of the addition formulas are also investigated.

• Journal of applied mathematics & informatics
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• v.38 no.3_4
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• pp.301-309
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• 2020

Recently, M. Masjed-Jamai et al. in ([6]-[7]) and Srivastava et al. in ([15]-[16]) considered the parametric type of the Apostol-Bernoulli, Apostol-Euler and Apostol-Genocchi polynomials. They proved some theorems and gave some identities and relations for these polynomials. In this work, we define the parametric poly-tangent numbers and polynomials. We give some relations and identities for the parametric poly-tangent polynomials.