Year: 2025
Type: article
Abstract: We construct two families of orthogonal polynomials associated with the universal central extensions of the superelliptic Lie algebras. These polynomials satisfy certain fourth-order linear differential equations, and one of the families is a particular collection of associated ultraspherical polynomials. We show that the generating functions of the polynomials satisfy fourth-order linear PDEs. Since these generating functions can be represented by superelliptic integrals, we have examples of linear PDEs of fourth order with explicit solutions without complete integrability.
Source: Forum of Mathematics Sigma
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $2,650
Funders: National Science Foundation, Universidade Federal do Amazonas, National Natural Science Foundation of China, Coordenação de Aperfeiçoamento de Pessoal de Nível Superior, Conselho Nacional de Desenvolvimento Científico e Tecnológico, Universidade Presbiteriana Mackenzie, National Natural Science Foundation of China-Henan Joint Fund
OpenAlex ID: W4413065807