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Zbl 0643.33009
Wimp, Jet
Explicit formulas for the associated Jacobi polynomials and some applications. (English)
[J] Can. J. Math. 39, No. 4, 983-1000 (1987). ISSN 0008-414X; ISSN 1496-4279/e

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 $c\ge 0$. In this well written paper, the author provides an explicit expression for the associated Jacobi polynomials, involving $\sb 4F\sb 3$ 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 $\alpha$, $\beta$. \par Finally, he provides a generating function, and derives a representation for the $n-1$, $n$ Padé approximant to $$ f(z): =F\left( \matrix a+1,b+1\\ c+1\endmatrix ;z\right)/F\left( \matrix a,b\\ c\endmatrix ;z\right).$$
[D.S.Lubinsky]

MSC 2000:: *33C45 Orthogonal polynomials and functions of hypergeometric type
33C05 Classical hypergeometric functions
41A21 Pade approximation

Keywords: associated Jacobi polynomials; Padé approximant

Cited in: Zbl 0797.33004

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