In this paper, we introduce the degenerate Laplace transform and degenerate gamma function and investigate some properties of the degenerate Laplace transform and degenerate gamma function. From our investigation, we derive some interesting formulas related to the degenerate Laplace transform and degenerate gamma function.

Degenerate Laplace transform and degenerate gamma function

In this paper, we introduce the degenerate Laplace transform and degenerate gamma function and investigate some of their properties. From our investigation, we derive some interesting formulas related to the degenerate Laplace transform and degenerate gamma function.

We derive a new matrix representation for higher-order Daehee numbers and polynomials, higher-order λ-Daehee numbers and polynomials, and twisted λ-Daehee numbers and polynomials of order k This helps us to obtain simple and short proofs of many previous results on higher-order Daehee numbers and polynomials Moreover, we obtain recurrence relations, explicit formulas, and some new results for these numbers and polynomials Furthermore, we investigate the relation between these numbers and polynomials and Stirling, Norlund, and Bernoulli numbers of higher-order Some numerical results and program are introduced using Mathcad for generating higher-order Daehee numbers and polynomials The results of this article generalize the results derived very recently by El-Desouky and Mustafa (Appl Math Sci 9(73):3593-3610, 2015)

/pdf/new-results-on-higher-order-daehee-and-bernoulli-numbers-and-3rei4wjeme.pdf

New results on higher-order Daehee and Bernoulli numbers and polynomials

L. Carlitz introduced higher order degenerate Euler polynomials in [4, 5] and studied a degenerate Staudt-Clausen theorem in [4]. D. S. Kim and T. Kim gave some formulas and identities of degenerate Euler polynomials which are derived from the fermionic p-adic integrals on Zp (see [9]). In this paper, we introduce higher order degenerate Genocchi polynomials. And we give some formulas and identities of degenerate Genocchi polynomials which are derived from the fermionic p-adic integrals on Zp.

http://koreascience.or.kr:80/article/JAKO201611962056672.pdf

Some identities of degenerate genocchi polynomials

Partial differential equations for a new family of numbers and polynomials unifying the Apostol-type numbers and the Apostol-type polynomials

Recently, Daehee numbers and polynomials are introduced by the authors In this paper, we consider the Daehee numbers and polynomials of order k (∈ N) and give some relation between Daehee polynomials of order k(∈ N) and special polynomials

/pdf/higher-order-daehee-numbers-and-polynomials-4up32wlonh.pdf

Higher-order Daehee numbers and polynomials

A note on the lambda-Daehee polynomials

In this paper, we consider Daehee polynomials with q-parameter and investigate some properties of those polynomials.

/pdf/daehee-polynomials-with-q-parameter-44bb8e2uaz.pdf

Daehee Polynomials with q-Parameter

Abstract In this paper, we introduce the new fully degenerate poly-Bernoulli numbers and polynomials and inverstigate some properties of these polynomials and numbers. From our properties, we derive some identities for the fully degenerate poly-Bernoulli numbers and polynomials.

https://www.degruyter.com/downloadpdf/j/math.2016.14.issue-1/math-2016-0048/math-2016-0048.xml

Fully degenerate poly-Bernoulli numbers and polynomials

Recently, the non-linear Changhee differential equations were introduced in [5] and these differential equations turned out to be very useful for studying special polynomials and mathematical physics. Some interesting identities and properties of Changhee polynomials can also be derived from umbral calculus (see [7]). In this paper, we consider differential equations arising from Changhee polynomials and derive some new and explicit formulae and identities from our differential equations.

/pdf/differential-equations-for-changhee-polynomials-and-their-wglwcjwcdb.pdf

Jong-Jin Seo

Papers

Higher-order Daehee numbers and polynomials

A note on the lambda-Daehee polynomials

Daehee Polynomials with q-Parameter

Fully degenerate poly-Bernoulli numbers and polynomials

Differential equations for Changhee polynomials and their applications