A new family of degenerate poly-bernoulli polynomials of the second kind with its certain related properties

Waseem A. Khan; Abdulghani Muhyi; Rifaqat Ali; Khaled Ahmad Hassan Alzobydi; Manoj Singh; Praveen Agarwal

doi:10.3934/math.2021731

A new family of degenerate poly-bernoulli polynomials of the second kind with its certain related properties

Waseem A. Khan
, Abdulghani Muhyi
, Rifaqat Ali
, Khaled Ahmad Hassan Alzobydi
, Manoj Singh
, Praveen Agarwal

Nonlinear Dynamic Research Centre (NDRC)

Prince Mohammad Bin Fahd University
Hajjah University
King Khalid University
Jazan University
International College of Engineering
International Center for Basic and Applied Sciences

Research output: Contribution to journal › Article › peer-review

36 Scopus citations

Abstract

The main object of this article is to present type 2 degenerate poly-Bernoulli polynomials of the second kind and numbers by arising from modified degenerate polyexponential function and investigate some properties of them. Thereafter, we treat the type 2 degenerate unipoly-Bernoulli polynomials of the second kind via modified degenerate polyexponential function and derive several properties of these polynomials. Furthermore, some new identities and explicit expressions for degenerate unipoly polynomials related to special numbers and polynomials are obtained. In addition, certain related beautiful zeros and graphical representations are displayed with the help of Mathematica.

Original language	English
Pages (from-to)	12680-12697
Number of pages	18
Journal	AIMS Mathematics
Volume	6
Issue number	11
DOIs	https://doi.org/10.3934/math.2021731
State	Published - 2021

Keywords

Degenerate unipoly functions
Modified degenerate polyexponential functions
Type 2 degenerate poly-Bernoulli polynomials of the second kind

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10.3934/math.2021731

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abstract = "The main object of this article is to present type 2 degenerate poly-Bernoulli polynomials of the second kind and numbers by arising from modified degenerate polyexponential function and investigate some properties of them. Thereafter, we treat the type 2 degenerate unipoly-Bernoulli polynomials of the second kind via modified degenerate polyexponential function and derive several properties of these polynomials. Furthermore, some new identities and explicit expressions for degenerate unipoly polynomials related to special numbers and polynomials are obtained. In addition, certain related beautiful zeros and graphical representations are displayed with the help of Mathematica.",

keywords = "Degenerate unipoly functions, Modified degenerate polyexponential functions, Type 2 degenerate poly-Bernoulli polynomials of the second kind",

author = "Khan, \{Waseem A.\} and Abdulghani Muhyi and Rifaqat Ali and Alzobydi, \{Khaled Ahmad Hassan\} and Manoj Singh and Praveen Agarwal",

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T1 - A new family of degenerate poly-bernoulli polynomials of the second kind with its certain related properties

AU - Khan, Waseem A.

AU - Muhyi, Abdulghani

AU - Ali, Rifaqat

AU - Alzobydi, Khaled Ahmad Hassan

AU - Singh, Manoj

AU - Agarwal, Praveen

PY - 2021

Y1 - 2021

N2 - The main object of this article is to present type 2 degenerate poly-Bernoulli polynomials of the second kind and numbers by arising from modified degenerate polyexponential function and investigate some properties of them. Thereafter, we treat the type 2 degenerate unipoly-Bernoulli polynomials of the second kind via modified degenerate polyexponential function and derive several properties of these polynomials. Furthermore, some new identities and explicit expressions for degenerate unipoly polynomials related to special numbers and polynomials are obtained. In addition, certain related beautiful zeros and graphical representations are displayed with the help of Mathematica.

AB - The main object of this article is to present type 2 degenerate poly-Bernoulli polynomials of the second kind and numbers by arising from modified degenerate polyexponential function and investigate some properties of them. Thereafter, we treat the type 2 degenerate unipoly-Bernoulli polynomials of the second kind via modified degenerate polyexponential function and derive several properties of these polynomials. Furthermore, some new identities and explicit expressions for degenerate unipoly polynomials related to special numbers and polynomials are obtained. In addition, certain related beautiful zeros and graphical representations are displayed with the help of Mathematica.

KW - Degenerate unipoly functions

KW - Modified degenerate polyexponential functions

KW - Type 2 degenerate poly-Bernoulli polynomials of the second kind

UR - https://www.scopus.com/pages/publications/85114336418

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SN - 2473-6988

VL - 6

SP - 12680

EP - 12697

JO - AIMS Mathematics

JF - AIMS Mathematics

IS - 11

ER -

A new family of degenerate poly-bernoulli polynomials of the second kind with its certain related properties

Abstract

Keywords

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