TWO CLASSES OF TWO DIMENSIONAL MIXED GEGENBAUER-LEGENDRE POLYNOMIALS TO APPLY IN COMPUTATION OF THE REGION OF CONVERGENCE OF ARBITRARY FUNCTION CONTAINING THEM
By
R. C. Singh Chandel¹ , Hemant Kumar² and P. K. Vishwakarma³
¹Former Head, Department of Mathematics D. V. Postgraduate College Orai, Uttar Pradesh, India285001
²Department of Mathematics, D. A-V. Postgraduate College Kanpur, Uttar Pradesh, India-208001
³Department of Mathematics, Atarra Postgraduate College Atarra, Uttar Pradesh, India-210201
Email: rc chandel@yahoo.com, palhemant2007@rediffmail.com, pkvncc.1965@yahoo.in
(Received: January 03, 2024; In format: March 24, 2024; Revised: April 11, 2024; Accepted: April 12, 2024)
DOI: https://doi.org/10.58250/jnanabha.2024.54118
Abstract
In this article we introduce interesting two dimensional formulae of Legendre and Gegenbauer polynomials and then study their analytic and algebraic properties to derive some known and unknown results. Again we define two classes of two dimensional Gegenbauer-Legendre polynomials to obtain their series formulae. Finally, we use these results in the computation of the region of convergence of arbitrary function consisting of Gegenbauer-Legendre mixed polynomials.
2020 Mathematical Sciences Classification: 33C45; 33C47; 11B39; 33C90.
Keywords and Phrases: Analytic and algebraic properties; Legendre and Gegenbauer polynomials; Gegenbauer-Legendre mixed polynomials; Computation of the region of convergence of any function consisting Gegenbauer-Legendre mixed polynomials.