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Zbl 0744.33007
Kalnins, E.G.; Miller, W.jun.
Hypergeometric expansions of Heun polynomials. (English)
[J] SIAM J. Math. Anal. 22, No.5, 1450-1459 (1991). ISSN 0036-1410; ISSN 1095-7154/e

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.
[H.Exton (Dunrossness)]

MSC 2000:: *33C80 Connections of theory of special functions with groups and algebras
22E70 Appl. of Lie groups to physics
33C45 Orthogonal polynomials and functions of hypergeometric type

Keywords: Heun polynomials; Jacobi polynomials; recurrence relation; expansion

Citations: Zbl 0602.35014

Cited in: Zbl 0828.33003

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