Lekesiz, Esra GüldoğanTefo, Yves GuemoAktas, RabiaArea, IvanLekesiz, Esra GuldoganMathematics2024-07-052024-07-05202211017-060X1735-851510.1007/s41980-021-00605-82-s2.0-85109830372https://doi.org/10.1007/s41980-021-00605-8https://hdl.handle.net/20.500.14411/1991Area, Ivan/0000-0003-0872-5017; Güldoğan Lekesiz, Esra/0000-0001-7653-8745; Aktas, Rabia/0000-0002-7811-8610A 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.eninfo:eu-repo/semantics/openAccessBivariate orthogonal polynomialsSymmetric orthogonal polynomialsPartial differential equationsArticleQ348416491665WOS:000672325700001