Certain unified polynomials. Issue 1 (2nd January 2019)

• Record Type: Journal Article
• Authors: Choi, Junesang; Khan, Nabiullah; Usman, Talha; Aman, Mohd
• Is Part Of: Integral transforms and special functions. Volume 30:Issue 1(2019)
• Page Start: 28
• Page End: 40
• Publication Date: 2019-01-02
• Subjects: Pell polynomials and numbers -- Pell-Lucas polynomials and numbers -- Fibonacci polynomials and numbers -- h(x)-Fibonacci polynomials -- Catalan polynomials -- h(x)-Fibonacci-Hermite polynomials -- Gegenbauer polynomials -- generalized hypergeometric series -- a generalization of the Kampé de Fériet function -- recurrence relations -- differential equation -- generating functions; 33B15 -- 33C05 -- 33C10 -- 33C15 -- 33C45 -- 33E20; Integral transforms -- Periodicals; Transcendental functions -- Periodicals; Transformations (Mathematics) -- Periodicals; Calculus, Integral -- Periodicals; 515
• DOI: 10.1080/10652469.2018.1534847
• Languages: English
• ISSNs: 1065-2469

Abstract

ABSTRACT: 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, andh ( x ) -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.