• Communications of the Korean Mathematical Society
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• v.35 no.3
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• pp.759-771
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• 2020

In this article, a hybrid class of the q-Hermite based Apostol type Frobenius-Genocchi polynomials is introduced by means of generating function and series representation. Several important formulas and recurrence relations for these polynomials are derived via different generating function methods. Furthermore, we consider some relationships for q-Hermite based Apostol type Frobenius-Genocchi polynomials of order α associated with q-Apostol Bernoulli polynomials, q-Apostol Euler polynomials and q-Apostol Genocchi polynomials.

• 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.35 no.5_6
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• pp.587-597
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• 2017

In this paper we define the (p, q)-analogue of Bernoulli numbers and polynomials by generalizing the Bernoulli numbers and polynomials, Carlitz's type q-Bernoulli numbers and polynomials. We also give some interesting properties, explicit formulas, a connection with (p, q)-analogue of Bernoulli numbers and polynomials. Finally, we investigate the zeros of the (p, q)-analogue of Bernoulli polynomials by using computer.

• Journal of Applied and Pure Mathematics
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• v.5 no.3_4
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• pp.165-186
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• 2023

In this paper we give some prperties of the (p, q)-poly-cosine tangent polynomials and (p, q)-poly-sine tangent polynomials.

• Journal of applied mathematics & informatics
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• v.31 no.3_4
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• pp.523-531
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• 2013

In this paper we construct a new type of $q$-Bernstein polynomials related to $q$-Euler numbers and polynomials with weak weight ${\alpha}$ ; $E^{(\alpha)}_{n,q}$, $E^{(\alpha)}_{n,q}(x)$ respectively. Some interesting results and relationships are obtained.

• Journal of applied mathematics & informatics
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• v.39 no.1_2
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• pp.83-91
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• 2021

In this paper, we introduce the concepts of q-cosine tangent polynomials and q-sine tangent polynomials. From these polynomials, we find some identities and properties by using q-numbers and q-trigonometric functions.

• East Asian mathematical journal
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• v.36 no.1
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• pp.13-24
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• 2020

The main purpose of this paper is to introduce Apostol type (p, q)-Frobenius-Genocchi numbers and polynomials of order α and investigate some basic identities and properties for these polynomials and numbers including addition theorems, difference equations, derivative properties, recurrence relations. We also obtain integral representations, implicit and explicit formulas and relations for these polynomials and numbers. Furthermore, we consider some relationships for Apostol type (p, q)-Frobenius-Genocchi polynomials of order α associated with (p, q)-Apostol Bernoulli polynomials, (p, q)-Apostol Euler polynomials and (p, q)-Apostol Genocchi polynomials.

• Journal of applied mathematics & informatics
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• v.37 no.3_4
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• pp.295-305
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• 2019

In the present paper, we introduce (p, q)-Frobenius-Genocchi numbers and polynomials and investigate some basic identities and properties for these polynomials and numbers including addition theorems, difference equations, derivative properties, recurrence relations and so on. Then, we provide integral representations, implicit and explicit formulas and relations for these polynomials and numbers. We consider some relationships for (p, q)-Frobenius-Genocchi polynomials of order ${\alpha}$ associated with (p, q)-Bernoulli polynomials, (p, q)-Euler polynomials and (p, q)-Genocchi polynomials.

• Communications of the Korean Mathematical Society
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• v.34 no.4
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• pp.1175-1199
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• 2019

We construct a general bi-basic inverse series relation which provides extension to several q-polynomials including the Askey-Wilson polynomials and the q-Racah polynomials. We introduce a general class of polynomials suggested by this general inverse pair which would unify certain polynomials such as the q-extended Jacobi polynomials and q-Konhauser polynomials. We then emphasize on applications of the general inverse pair and obtain the generating function relations, summation formulas involving the associated polynomials and derive the p-deformation of some of the q-analogues of Riordan's classes of inverse series relations. We also illustrate the companion matrix corresponding to the general class of polynomials; this is followed by a chart showing the reducibility of the extended p-deformed Askey-Wilson polynomials as well as the extended p-deformed q-Racah polynomials.

• Journal of applied mathematics & informatics
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• v.39 no.1_2
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• pp.57-72
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• 2021

In this paper, we construct q-cosine and sine Genocchi polynomials using q-analogues of addition, subtraction, and q-trigonometric function. From these polynomials, we obtain some properties and identities. We investigate some symmetric properties of q-cosine and sine Genocchi polynomials. Moreover, we find relations between these polynomials and others polynomials.