• Honam Mathematical Journal
• /
• v.41 no.4
• /
• pp.781-798
• /
• 2019

This paper is designed to introduce a Hermite-based-poly-Bernoulli numbers and polynomials with q-parameter. By making use of their generating functions, we derive several summation formulae, identities and some properties that is connected with the Stirling numbers of the second kind. Furthermore, we derive symmetric identities for Hermite-based-poly-Bernoulli polynomials with q-parameter by using generating functions.

• Journal of applied mathematics & informatics
• /
• v.41 no.6
• /
• pp.1303-1315
• /
• 2023

In this paper, the degenerate q-Bernoulli polynomials are defined by generalizing it more, and various properties of these polynomials are introduced. To do this, we define generating functions of them and use the definition to introduce some interesting properties. Finally, we observe the structure of the roots for the degenerate q-Bernoulli polynomials.

• Communications of the Korean Mathematical Society
• /
• v.12 no.3
• /
• pp.603-617
• /
• 1997

Consider a Sobolev inner product on the space of polynomials such as $$ \phi(p,q) = \lambda p(c)q(c) + <\tau,p'(x)q'(x)> $$ where $\tau$ is a moment functional and c and $\lambda$ are real constants. We investigate properties of orthogonal polynomials relative to $\phi(\cdot,\cdot)$ and give necessary and sufficient conditions under which such Sobolev orthogonal polynomials satisfy a spectral type differential equation with polynomial coefficients.

• Bulletin of the Korean Mathematical Society
• /
• v.53 no.4
• /
• pp.1149-1156
• /
• 2016

In this paper, we introduce the degenerate Carlitz q-Bernoulli numbers and polynomials and give some interesting identities and properties of these numbers and polynomials which are derived from the generating functions and p-adic integral equations.

• Journal of Applied and Pure Mathematics
• /
• v.5 no.5_6
• /
• pp.291-301
• /
• 2023

In this paper, we investigate the zeros of the fully modified q-poly-tangent polynomials of the first type.

• Journal of applied mathematics & informatics
• /
• v.35 no.1_2
• /
• pp.205-215
• /
• 2017

In this paper, we consider a modified Euler polynomials ${\tilde{E}}_{n,q}(x)$ with variable $[x]_q$ and investigate some interesting properties of the Euler polynomials. We also give some relationships between the modified Euler polynomials and their Hurwitz zeta function. Finally, we derive some identities associated with Bernstein polynomials.

• Journal of applied mathematics & informatics
• /
• v.35 no.5_6
• /
• pp.611-621
• /
• 2017

In this paper, we define a q-analogue of the poly-Bernoulli numbers and polynomials which is generalization of the poly Bernoulli numbers and polynomials including q-polylogarithm function. We also give the relations between generalized poly-Bernoulli polynomials. We derive some relations that are connected with the Stirling numbers of second kind. By using special functions, we investigate some symmetric identities involving q-poly-Bernoulli polynomials.

• Journal of applied mathematics & informatics
• /
• v.38 no.5_6
• /
• pp.611-623
• /
• 2020

In this paper, we define a q-analogue of the poly-Euler numbers and polynomials which is generalization of the poly Euler numbers and polynomials including q-analogue of polylogarithm function. We also give the relations between generalized poly-Euler polynomials. Furthermore, we introduce zeta fuctions of Arakawa-Kaneko type and talk their properties and the relation with q-analogue of poly-Euler polynomials.

• Journal of the Korean Mathematical Society
• /
• v.48 no.5
• /
• pp.913-926
• /
• 2011

The family of q-Laguerre polynomials $\{L_n^{(\alpha)}({\cdot};q)\}_{n=0}^{\infty}$ is usually defined for 0 < q < 1 and ${\alpha}$ > -1. We extend this family to a new one in which arbitrary complex values of the parameter ${\alpha}$ are allowed. These so-called generalized q-Laguerre polynomials fulfil the same three term recurrence relation as the original ones, but when the parameter ${\alpha}$ is a negative integer, no orthogonality property can be deduced from Favard's theorem. In this work we introduce non-standard inner products involving q-derivatives with respect to which the generalized q-Laguerre polynomials $\{L_n^{(-N)}({\cdot};q)\}_{n=0}^{\infty}$, for positive integers N, become orthogonal.

• Journal of applied mathematics & informatics
• /
• v.34 no.1_2
• /
• pp.107-114
• /
• 2016

In this paper we give some symmetric property of the generalized twisted q-Euler zeta functions and q-Euler polynomials.