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Symmetric Jacobi polynomials used in the orthogonal collocation method can be obtained from

,

where applies to a rectangular, cylindrical, or spherical coordinate, respectively, is the hypergeometric function, is the order in the polynomial, is the Jacobi polynomial, and is the independent variable.

Reference: J. V. Villadsen and W. E. Stewart, "Solution of Boundary-Value Problems by Orthogonal Collocation," Chemical Engineering Science, 22, 1967 pp. 3981–3996.