Properties and Graphical Representations of the 2-Variable Form of the Simsek Polynomials

This article is written with an objective to introduce the 2-variable Simsek polynomials Y n ( x , y ; λ , δ ) and to investigate some properties of these polynomials. The 2-variable forms of Changhee and Daehee polynomials are also considered. Several important recurrence relations involving the Ca...

Full description

Saved in:
Bibliographic Details
Published in:Vietnam journal of mathematics 2022, Vol.50 (1), p.95-109
Main Authors: Khan, Subuhi, Nahid, Tabinda, Riyasat, Mumtaz
Format: Article
Language:English
Subjects:
Graphical representations
Hypergeometric functions
Mathematics
Mathematics and Statistics
Nonlinear differential equations
Numbers
Original Article
Polynomials
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:This article is written with an objective to introduce the 2-variable Simsek polynomials Y n ( x , y ; λ , δ ) and to investigate some properties of these polynomials. The 2-variable forms of Changhee and Daehee polynomials are also considered. Several important recurrence relations involving the Cauchy, Changhee, Daehee and Simsek numbers are derived. The hypergeometric function representation for an integral involving these polynomials is obtained. The graphical representations of the 2-variable Simsek polynomials are considered for suitable values of the index n and parameters λ and δ . The article is concluded with the derivation of non-linear differential equation and related identity for the Simsek numbers.
ISSN:2305-221X
2305-2228
DOI:10.1007/s10013-020-00472-6