Certain unified polynomials

We aim to introduce certain unified polynomials which can be specialized to yield a number of known polynomials and numbers, for example, Pell polynomials and numbers, Fibonacci polynomials and numbers, and -Fibonacci polynomials. Then we investigate the unified polynomials to present certain intere...

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Bibliographic Details
Published in:Integral transforms and special functions Vol. 30; no. 1; pp. 28 - 40
Main Authors: Choi, Junesang, Khan, Nabiullah, Usman, Talha, Aman, Mohd
Format: Journal Article
Language:English
Published: Abingdon Taylor & Francis 02.01.2019
Taylor & Francis Ltd
Subjects:
a generalization of the Kampé de Fériet function
Catalan polynomials
differential equation
Differential equations
Fibonacci numbers
Fibonacci polynomials
Fibonacci polynomials and numbers
Fibonacci-Hermite polynomials
Functions (mathematics)
Gegenbauer polynomials
generalized hypergeometric series
generating functions
Mathematical analysis
Pell polynomials and numbers
Pell-Lucas polynomials and numbers
Polynomials
recurrence relations
ISSN:1065-2469, 1476-8291
Online Access:Get full text
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Summary:We aim to introduce certain unified polynomials which can be specialized to yield a number of known polynomials and numbers, for example, Pell polynomials and numbers, Fibonacci polynomials and numbers, and -Fibonacci polynomials. Then we investigate the unified polynomials to present certain interesting and potentially useful properties such as explicit expressions, some recurrence relations, a differential equation, and several generating functions. Further, among a number of polynomials and numbers which can be specialized from the unified polynomials, we choose the Pell polynomials to record their corresponding properties.
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content type line 14
ISSN:1065-2469
1476-8291
DOI:10.1080/10652469.2018.1534847