Tokyo Journal of Mathematics

$q$-Extension of a Multivariable and Multiparameter Generalization of the Gottlieb Polynomials in Several Variables

Abstract

While considering some families of polynomials which are orthogonal on a finite or enumerable set of points, Gottlieb was led in the year 1938 to what are now popularly known as the Gottlieb polynomials $\varphi_n(x;\lambda)$. This one-parameter family of polynomials has ever since then been cited widely and investigated extensively in several books, monographs and journal articles. In the present sequel to some of the aforementioned investigations, we introduce and systematically investigate a basic (or $q$-) extension of a multivariable and multiparameter generalization of the Gottlieb polynomials $\varphi_n(x;\lambda)$. We also establish a set of three new families of generating functions for the generalized $q$-Gottlieb polynomials defined here.

Article information

Source
Tokyo J. Math., Volume 37, Number 1 (2014), 111-125.

Dates
First available in Project Euclid: 28 July 2014

https://projecteuclid.org/euclid.tjm/1406552433

Digital Object Identifier
doi:10.3836/tjm/1406552433

Mathematical Reviews number (MathSciNet)
MR3264516

Zentralblatt MATH identifier
1300.33008

Citation

CHOI, Junesang; SRIVASTAVA, H. M. $q$-Extension of a Multivariable and Multiparameter Generalization of the Gottlieb Polynomials in Several Variables. Tokyo J. Math. 37 (2014), no. 1, 111--125. doi:10.3836/tjm/1406552433. https://projecteuclid.org/euclid.tjm/1406552433

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