Hypergeometric Expansions of Heun Polynomials

DOI10.1137/0522093zbMath0744.33007OpenAlexW2005378468MaRDI QIDQ3982751

Ernest G. Kalnins, Willard jun. Miller

Publication date: 26 June 1992

Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)

Full work available at URL: http://purl.umn.edu/1386

zbMATH Keywords

Heun polynomialsexpansionrecurrence relationJacobi polynomials

Mathematics Subject Classification ID

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Connections of hypergeometric functions with groups and algebras, and related topics (33C80) Applications of Lie groups to the sciences; explicit representations (22E70)

Related Items (11)

Superintegrability and associated polynomial solutions: Euclidean space and the sphere in two dimensions ⋮ The third five-parametric hypergeometric quantum-mechanical potential ⋮ Expansions of the solutions of the general Heun equation governed by two-term recurrence relations for coefficients ⋮ Separation equations for 2D superintegrable systems on constant curvature spaces ⋮ Schrödinger potentials solvable in terms of the general Heun functions ⋮ Tridiagonalization and the Heun equation ⋮ Superintegrability on the two-dimensional hyperboloid ⋮ The Liouville–Neumann approximation of the regular solutions of the Heun's equations ⋮ Orthogonal polynomials, asymptotics, and Heun equations ⋮ Expansions of the solutions of the confluent Heun equation in terms of the incomplete Beta and the Appell generalized hypergeometric functions ⋮ SERIES SOLUTIONS OF CONFLUENT HEUN EQUATIONS IN TERMS OF INCOMPLETE GAMMA-FUNCTIONS

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