• Journal of applied mathematics & informatics
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• v.27 no.3_4
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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 $G_{n,x}(x)$.

• Kyungpook Mathematical Journal
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• v.55 no.3
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• pp.597-614
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• 2015

In this paper, we study some properties of the generalized Apostol type Hermite-based polynomials. which extend some known results. We also deduce some properties of the generalized Apostol-Bernoulli polynomials, the generalized Apostol-Euler polynomials and the generalized Apostol-Genocchi polynomials of high order. Numerous properties of these polynomials and some relationships between $F_n{^{({\alpha})}}(x;{\lambda};{\mu};{\nu};c)$ and $_HF_n{^{({\alpha})}}(x;{\lambda};{\mu};{\nu};c)$ are established. Some implicit summation formulae and general symmetry identities are derived by using different analytical means and applying generating functions.

• Bulletin of the Korean Mathematical Society
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• v.36 no.1
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• pp.161-169
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• 1999

Generalized nonnegative trigonometric polynomials are defined as the products of nonnegative trigonometric polynomials raised to positive real powers. The generalized degree can be defined in a natural way. We improve and extend the large sieve involving pth powers of trigonometric polynomials so that it holds for generalized trigonometric polynomials.

• Communications of the Korean Mathematical Society
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• v.25 no.2
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• pp.215-224
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• 2010

Generalized nonnegative polynomials are defined as products of nonnegative polynomials raised to positive real powers. The generalized degree can be defined in a natural way. In this paper we extend quadrature sums involving pth powers of polynomials to those for generalized polynomials.

• Journal of applied mathematics & informatics
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• v.38 no.1_2
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• pp.159-173
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• 2020

In this paper we define a new generalized polynomials of derangements. It also derives the differential equations that occur in the generating function of the generalized polynomials of derangements. We establish some new identities for the generalized polynomials of derangements. Finally, we perform a survey of the distribution of zeros of the generalized polynomials of derangements.

• Communications of the Korean Mathematical Society
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• v.36 no.2
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• pp.239-246
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• 2021

In this article, a study of generalized Bateman's matrix polynomials is presented. We obtained partial differential equations by using differential operators in the generalized Bateman's matrix polynomials for two variables. Then we introduced some different recurrence relationships of the generalized Bateman's matrix polynomials. Finally present the relationship between the generalized Bateman's matrix polynomials of one and two variables.

• Bulletin of the Korean Mathematical Society
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• v.41 no.2
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• pp.299-306
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• 2004

In this paper, we shall construct generating function of twisted generalized Euler numbers. By using this function, we shall define twisted generalized Euler polynomials and numbers. We shall give some basic properties of these polynomials and numbers.

• Honam Mathematical Journal
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• v.34 no.3
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• pp.311-326
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• 2012

The purpose of this paper is to introduce and investigate two new classes of generalized Bernoulli and Apostol-Bernoulli polynomials based on the definition given recently by the authors [29]. In particular, we obtain a new addition formula for the new class of the generalized Bernoulli polynomials. We also give an extension and some analogues of the Srivastava-Pint$\acute{e}$r addition theorem [28] for both classes. Finally, by making use of the new adition formula, we exhibit several interesting relationships between generalized Bernoulli polynomials and other polynomials or special functions.

• Journal of applied mathematics & informatics
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• v.38 no.3_4
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• pp.211-220
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• 2020

In this paper, we introduce and investigate a new class of generalized polynomials associated with Hermite-Bernoulli polynomials of higher order. This generalization is a unification formula of Bernoulli numbers, Bernoulli polynomials, Hermite-Bernoulli polynomials of Dattoli, generalized Hermite-Bernoulli polynomials for two variables of order α and new other families of polynomials depending on any generating function f.

• Journal of applied mathematics & informatics
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• v.36 no.1_2
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• pp.115-120
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• 2018

In this paper, we discover symmetric properties for generalized Carlitz's q-tangent polynomials.