Kalnins, Ernie G.Miller, W., Jr.2019-02-251991-09-012019-02-251991Kalnins, E. G., & Miller, W., Jr. (1991). Hypergeometric expansions of Heun polynomials. SIAM Journal on Mathematical Analysis, 22(5), 1450–1459. https://doi.org/10.1137/05220930036-1410https://hdl.handle.net/10289/12368The product of two Heun polynomials is expanded in terms of products of two Jacobi polynomials. This is done by making crucial use of group theory and the knowledge of separable coordinate systems on the n-sphere. The expansion presented includes as a special case hypergeometric function expansions of single Heun polynomials that have been derived previously by other methods.application/pdfenCopyright © 1991 Society for Industrial and Applied MathematicsScience & TechnologyPhysical SciencesMathematics, AppliedMathematicsmultivariable orthogonal polynomialsthe N-SphereHeun functionsseparationVariablesJournal Article10.1137/0522093