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Hypergeometric expansions of Heun polynomials. (English) Zbl 0744.33007
The graphical calculus of separable coordinates for the Laplace-Beltrami eigenvalue equation on the $n$-sphere [the authors, J. Math. Phys. 27, 1721-1736 (1986; Zbl 0602.35014)] is used to derive expansions of a product of Heun polynomials in series of products of Jacobi polynomials. The coefficients of this expansion satisfy a three-term recurrence relation. If one of the variables is fixed, then we have an expansion for single Heun polynomials.

33C80Connections of hypergeometric functions with groups and algebras
22E70Applications of Lie groups to physics; explicit representations
33C45Orthogonal polynomials and functions of hypergeometric type
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