• Journal of applied mathematics & informatics
• /
• 제37권3_4호
• /
• pp.317-328
• /
• 2019

This paper defines Carlitz's type (p, q)-Genocchi polynomials and Carlitz's type (h, p, q)-Genocchi polynomials, and explains fourteen properties which can be complemented by Carlitz's type (p, q)-Genocchi polynomials and Carlitz's type (h, p, q)-Genocchi polynomials, including distribution relation, symmetric property, and property of complement. Also, it explores alternating powers sums by proving symmetric property related to Carlitz's type (p, q)-Genocchi polynomials.

• Journal of applied mathematics & informatics
• /
• 제39권1_2호
• /
• pp.57-72
• /
• 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.

• Journal of applied mathematics & informatics
• /
• 제39권1_2호
• /
• pp.1-11
• /
• 2021

In this paper, we define degenerate Carlitz-type twisted q-Euler numbers and polynomials by generalizing the degenerate Euler numbers and polynomials, Carlitz's type degenerate q-Euler numbers and polynomials. We also give some interesting properties, explicit formulas, symmetric properties, a connection with degenerate Carlitz-type twisted q-Euler numbers and polynomials.

• 대한수학회논문집
• /
• 제38권4호
• /
• pp.1175-1189
• /
• 2023

The main purpose of this paper is to give some new identities and properties related to Bernoulli type numbers and polynomials associated with the Bessel function of the first kind. We give symmetric properties of the Bernoulli type numbers and polynomials. Moreover, using generating functions and the Faà di Bruno's formula, we derive some new formulas and relations related to not only these polynomials, but also the Bernoulli numbers and polynomials and the Euler numbers and polynomials.

• Journal of applied mathematics & informatics
• /
• 제36권1_2호
• /
• pp.115-120
• /
• 2018

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

• 대한수학회보
• /
• 제36권1호
• /
• pp.161-169
• /
• 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.

• 대한수학회논문집
• /
• 제25권2호
• /
• pp.215-224
• /
• 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.

• 호남수학학술지
• /
• 제33권2호
• /
• pp.173-179
• /
• 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
• /
• 제36권3_4호
• /
• pp.205-212
• /
• 2018

In this paper, we study linear differential equations arising from the generating functions of twisted (h, q)-tangent polynomials. We give explicit identities for the twisted (h, q)-tangent polynomials.

• Journal of applied mathematics & informatics
• /
• 제22권1_2호
• /
• pp.125-132
• /
• 2006

It is the aim of this paper to introduce the Genocchi numbers Gn and polynomials Gn(x) and to display the shape of Genocchi polynomials Gn(x). Finally, we investigate the roots of the Genocchi polynomials Gn(x).