scholarly journals A Note on Type-Two Degenerate Poly-Changhee Polynomials of the Second Kind

Symmetry ◽  
2021 ◽  
Vol 13 (4) ◽  
pp. 579
Author(s):  
Dmitry V. Dolgy ◽  
Waseem A. Khan
Keyword(s):  
Changhee Polynomials

In this paper, we first define type-two degenerate poly-Changhee polynomials of the second kind by using modified degenerate polyexponential functions. We derive new identities and relations between type-two degenerate poly-Changhee polynomials of the second kind. Finally, we derive type-two degenerate unipoly-Changhee polynomials of the second kind and discuss some of their identities.

scholarly journals Notes on the Poly-Korobov polynomials and related polynomials

Filomat ◽  
2020 ◽  
Vol 34 (2) ◽  
pp. 469-474
Author(s):  
Burak Kurt
Keyword(s):  
Stirling Numbers ◽  
Bernoulli Numbers ◽  
Euler Polynomials ◽  
Changhee Polynomials

In recent years, many mathematicians ([2], [7], [8], [9], [15], [16], [21]) introduced and investigated for the Korobov polynomials. They gave some identities and relations for the Korobov type polynomials. In this work, we give some relations for the first kind Korobov polynomials and Korobov type Changhee polynomials. Further, wegive two relations between the poly-Changhee polynomials and the poly-Korobov polynomials. Also, we give a relation among the poly-Korobov type Changhee polynomials, the Stirling numbers of the second kind, the Euler polynomials and the Bernoulli numbers.

scholarly journals On Appell-type Changhee polynomials and numbers

2016 ◽  
Vol 2016 (1) ◽  
Author(s):  
Jeong Gon Lee ◽  
Lee-Chae Jang ◽  
Jong-Jin Seo ◽  
Sang-Ki Choi ◽  
Hyuck In Kwon
Keyword(s):  
Changhee Polynomials

scholarly journals Truncated-Exponential-Based Appell-Type Changhee Polynomials

Symmetry ◽  
2020 ◽  
Vol 12 (10) ◽  
pp. 1588
Author(s):  
Tabinda Nahid ◽  
Parvez Alam ◽  
Junesang Choi
Keyword(s):  
Recurrence Relations ◽  
Explicit Representation ◽  
Integral Inequalities ◽  
Exponential Polynomials ◽  
Integral Formulas ◽  
Open Questions ◽  
Changhee Polynomials ◽  
Natural Way ◽  
Addition Formulas

The truncated exponential polynomials em(x) (1), their extensions, and certain newly-introduced polynomials which combine the truncated exponential polynomials with other known polynomials have been investigated and applied in various ways. In this paper, by incorporating the Appell-type Changhee polynomials Chn*(x) (10) and the truncated exponential polynomials in a natural way, we aim to introduce so-called truncated-exponential-based Appell-type Changhee polynomials eCn*(x) in Definition 1. Then, we investigate certain properties and identities for these new polynomials such as explicit representation, addition formulas, recurrence relations, differential and integral formulas, and some related inequalities. We also present some integral inequalities involving these polynomials eCn*(x). Further we discuss zero distributions of these polynomials by observing their graphs drawn by Mathematica. Lastly some open questions are suggested.

scholarly journals Symmetry Identities of Changhee Polynomials of Type Two

Symmetry ◽  
2018 ◽  
Vol 10 (12) ◽  
pp. 740 ◽  
Author(s):  
Joohee Jeong ◽  
Dong-Jin Kang ◽  
Seog-Hoon Rim
Keyword(s):  
Recent Work ◽  
Changhee Polynomials

In this paper, we consider Changhee polynomials of type two, which are motivated from the recent work of D. Kim and T. Kim. We investigate some symmetry identities for the Changhee polynomials of type two which are derived from the properties of symmetry for the fermionic p-adic integral on Z p .

A note on twisted Changhee polynomials and numbers with weight

2015 ◽  
Vol 9 ◽  
pp. 1517-1525
Author(s):  
G. Y. Sohn ◽  
J. K. Kwon
Keyword(s):  
Changhee Polynomials

A note on weighted Changhee polynomials and numbers

2015 ◽  
Vol 9 ◽  
pp. 191-198
Author(s):  
Jongkyum Kwon ◽  
HyeonSeok Noh ◽  
SuHwan Jeong ◽  
AuJin Kim ◽  
JinHyeok Lee ◽  
...  
Keyword(s):  
Changhee Polynomials

On applications for Mahler expansion associated with p-adic q-integrals

2019 ◽  
Vol 15 (01) ◽  
pp. 67-84 ◽  
Author(s):  
Ugur Duran ◽  
Mehmet Acikgoz
Keyword(s):  
Explicit Formula ◽  
Gamma Function ◽  
Recurrence Relations ◽  
Stirling Numbers ◽  
Euler Polynomials ◽  
Symmetric Relation ◽  
Euler Constant ◽  
Basic Properties ◽  
Changhee Polynomials

In this paper, we primarily consider a generalization of the fermionic [Formula: see text]-adic [Formula: see text]-integral on [Formula: see text] including the parameters [Formula: see text] and [Formula: see text] and investigate its some basic properties. By means of the foregoing integral, we introduce two generalizations of [Formula: see text]-Changhee polynomials and numbers as [Formula: see text]-Changhee polynomials and numbers with weight [Formula: see text] and [Formula: see text]-Changhee polynomials and numbers of second kind with weight [Formula: see text]. For the mentioned polynomials, we obtain new and interesting relationships and identities including symmetric relation, recurrence relations and correlations associated with the weighted [Formula: see text]-Euler polynomials, [Formula: see text]-Stirling numbers of the second kind and Stirling numbers of first and second kinds. Then, we discover multifarious relationships among the two types of weighted [Formula: see text]-Changhee polynomials and [Formula: see text]-adic gamma function. Also, we compute the weighted fermionic [Formula: see text]-adic [Formula: see text]-integral of the derivative of [Formula: see text]-adic gamma function. Moreover, we give a novel representation for the [Formula: see text]-adic Euler constant by means of the weighted [Formula: see text]-Changhee polynomials and numbers. We finally provide a quirky explicit formula for [Formula: see text]-adic Euler constant.

On the Barnes-type Changhee polynomials

2015 ◽  
Vol 9 ◽  
pp. 6077-6082
Author(s):  
SangJo Yun ◽  
Jongkyum Kwon
Keyword(s):  
Changhee Polynomials

scholarly journals Symmetric Properties of Carlitz’s Type q-Changhee Polynomials

Symmetry ◽  
2018 ◽  
Vol 10 (11) ◽  
pp. 634 ◽  
Author(s):  
Yunjae Kim ◽  
Byung Kim ◽  
Jin-Woo Park
Keyword(s):  
Symmetry Group ◽  
Symmetric Identities ◽  
Changhee Polynomials ◽  
Symmetric Properties

Changhee polynomials were introduced by Kim, and the generalizations of these polynomials have been characterized. In our paper, we investigate various interesting symmetric identities for Carlitz’s type q-Changhee polynomials under the symmetry group of order n arising from the fermionic p-adic q-integral on Z p .

scholarly journals Differential equations associated with lambda-Changhee polynomials

2016 ◽  
Vol 09 (05) ◽  
pp. 3098-3111 ◽  
Author(s):  
Taekyun Kim ◽  
Dae San Kim ◽  
Jong-Jin Seo ◽  
Hyuck-In Kwon
Keyword(s):  
Differential Equations ◽  
Changhee Polynomials
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