scholarly journals Some identities of degenerate special polynomials

2015 ◽  
Vol 13 (1) ◽  
Author(s):  
Dae San Kim ◽  
Taekyun Kim
Keyword(s):  
Mixed Type ◽  
Higher Order ◽  
Euler Polynomials ◽  
Special Polynomials ◽  
Order Degenerate

AbstractIn this paper, by considering higher-order degenerate Bernoulli and Euler polynomials which were introduced by Carlitz, we investigate some properties of mixed-type of those polynomials. In particular, we give some identities of mixed-type degenerate special polynomials which are derived from the fermionic integrals on Z

Higher-order degenerate Euler polynomials

2015 ◽  
Vol 9 ◽  
pp. 57-73 ◽  
Author(s):  
Dae San Kim ◽  
Taekyun Kim
Keyword(s):  
Higher Order ◽  
Euler Polynomials ◽  
Order Degenerate

An identity of symmetry for the degenerate Frobenius-Euler Polynomials

2018 ◽  
Vol 68 (1) ◽  
pp. 239-243 ◽  
Author(s):  
Taekyun Kim ◽  
Dae San Kim
Keyword(s):  
Recurrence Relations ◽  
Higher Order ◽  
Euler Polynomials ◽  
Type Result ◽  
Order Degenerate ◽  
Multiplication Theorem

Abstract In this paper, we prove an identity of symmetry for the higher-order degenerate Frobenius-Euler polynomials and derive the recurrence relations and multiplication theorem type result for the degenerate Frobenius-Euler polynomials.

scholarly journals Some Relations of Two Type 2 Polynomials and Discrete Harmonic Numbers and Polynomials

Symmetry ◽  
2020 ◽  
Vol 12 (6) ◽  
pp. 905 ◽  
Author(s):  
Taekyun Kim ◽  
Dae San Kim
Keyword(s):  
Zeta Functions ◽  
Stirling Numbers ◽  
Higher Order ◽  
High Order ◽  
Euler Polynomials ◽  
Harmonic Numbers ◽  
Order Degenerate ◽  
Riemann Zeta ◽  
Changhee Polynomials

Harmonic numbers appear, for example, in many expressions involving Riemann zeta functions. Here, among other things, we introduce and study discrete versions of those numbers, namely the discrete harmonic numbers. The aim of this paper is twofold. The first is to find several relations between the Type 2 higher-order degenerate Euler polynomials and the Type 2 high-order Changhee polynomials in connection with the degenerate Stirling numbers of both kinds and Jindalrae–Stirling numbers of both kinds. The second is to define the discrete harmonic numbers and some related polynomials and numbers, and to derive their explicit expressions and an identity.

scholarly journals On the type 2 poly-Bernoulli polynomials associated with umbral calculus

2021 ◽  
Vol 19 (1) ◽  
pp. 878-887
Author(s):  
Taekyun Kim ◽  
Dae San Kim ◽  
Dmitry V. Dolgy ◽  
Jin-Woo Park
Keyword(s):  
Bernoulli Polynomials ◽  
Higher Order ◽  
Umbral Calculus ◽  
Euler Polynomials ◽  
Special Polynomials

Abstract Type 2 poly-Bernoulli polynomials were introduced recently with the help of modified polyexponential functions. In this paper, we investigate several properties and identities associated with those polynomials arising from umbral calculus techniques. In particular, we express the type 2 poly-Bernoulli polynomials in terms of several special polynomials, like higher-order Cauchy polynomials, higher-order Euler polynomials, and higher-order Frobenius-Euler polynomials.

scholarly journals Some explicit identities for the modified higher-order degenerate q-Euler polynomials and their zeroes

2017 ◽  
Vol 10 (05) ◽  
pp. 2524-2538
Author(s):  
Lee-Chae Jang ◽  
Byung Moon Kim ◽  
Sang-Ki Choi ◽  
C. S. Ryoo ◽  
D. V. Dolgy
Keyword(s):  
Higher Order ◽  
Euler Polynomials ◽  
Order Degenerate

scholarly journals New type of degenerate Daehee polynomials of the second kind

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Sunil Kumar Sharma ◽  
Waseem A. Khan ◽  
Serkan Araci ◽  
Sameh S. Ahmed
Keyword(s):  
Generating Function ◽  
Special Class ◽  
Stirling Numbers ◽  
Bernoulli Numbers ◽  
Higher Order ◽  
Bernoulli Numbers And Polynomials ◽  
New Type ◽  
Order Degenerate ◽  
Math Phys

Abstract Recently, Kim and Kim (Russ. J. Math. Phys. 27(2):227–235, 2020) have studied new type degenerate Bernoulli numbers and polynomials by making use of degenerate logarithm. Motivated by (Kim and Kim in Russ. J. Math. Phys. 27(2):227–235, 2020), we consider a special class of polynomials, which we call a new type of degenerate Daehee numbers and polynomials of the second kind. By using their generating function, we derive some new relations including the degenerate Stirling numbers of the first and second kinds. Moreover, we introduce a new type of higher-order degenerate Daehee polynomials of the second kind. We also derive some new identities and properties of this type of polynomials.

scholarly journals Certain results of hybrid families of special polynomials associated with appell sequences

Filomat ◽  
2019 ◽  
Vol 33 (12) ◽  
pp. 3833-3844 ◽  
Author(s):  
Ghazala Yasmin ◽  
Abdulghani Muhyi
Keyword(s):  
Generating Functions ◽  
Mixed Type ◽  
Bernoulli Polynomials ◽  
Operational Method ◽  
Appell Polynomials ◽  
Special Polynomials ◽  
Appell Sequences

In this article, the Legendre-Gould-Hopper polynomials are combined with Appell sequences to introduce certain mixed type special polynomials by using operational method. The generating functions, determinant definitions and certain other properties of Legendre-Gould-Hopper based Appell polynomials are derived. Operational rules providing connections between these formulae and known special polynomials are established. The 2-variable Hermite Kamp? de F?riet based Bernoulli polynomials are considered as an member of Legendre-Gould-Hopper based Appell family and certain results for this member are also obtained.

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