Browsing by Author "Area, Ivan"

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Citation - WoS: 4
Citation - Scopus: 5
A New Family of Orthogonal Polynomials in Three Variables
(Springer, 2020) Aktas, Rabia; Area, Ivan; Guldogan, Esra
In this paper we introduce a six-parameter generalization of the four-parameter three-variable polynomials on the simplex and we investigate the properties of these polynomials. Sparse recurrence relations are derived by using ladder relations for shifted univariate Jacobi polynomials and bivariate polynomials on the triangle. Via these sparse recurrence relations, second order partial differential equations are presented. Some connection relations are obtained between these polynomials. Also, new results for the four-parameter three-variable polynomials on the simplex are given. Finally, some generating functions are derived.
Citation - WoS: 1
Citation - Scopus: 1
On a Symmetric Generalization of Bivariate Sturm-Liouville Problems
(Springer Singapore Pte Ltd, 2022) Tefo, Yves Guemo; Aktas, Rabia; Area, Ivan; Lekesiz, Esra Guldogan
A new class of partial differential equations having symmetric orthogonal solutions is presented. The general equation is presented and orthogonality is obtained using the Sturm-Liouville approach. Conditions on the polynomial coefficients to have admissible partial differential equations are given. The general case is analyzed in detail, providing orthogonality weight function, three-term recurrence relations for the monic orthogonal polynomial solutions, as well as explicit form of these monic orthogonal polynomial solutions, which are solutions of an admissible and potentially self-adjoint linear second-order partial differential equation of hypergeometric type.