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Explicit formulas for the associated Jacobi polynomials and some applications. (English) Zbl 0643.33009

The associated Jacobi polynomials are the polynomials satisfying the same recurrence relation as the Jacobi polynomials, but with n replaced by n+c, for some fixed c0. In this well written paper, the author provides an explicit expression for the associated Jacobi polynomials, involving 4 F 3 hypergeometric functions. He also determines explicitly the weight function with respect to which these polynomials are orthogonal, under mild restrictions on c and the Jacobi parameters α, β.

Finally, he provides a generating function, and derives a representation for the n-1, n Padé approximant to


Reviewer: D.S.Lubinsky

33C45Orthogonal polynomials and functions of hypergeometric type
33C05Classical hypergeometric functions, 2 F 1
41A21Padé approximation