Title

Jacobi polynomials from compatibility conditions

Authors

Authors

Y. Chen;M. Ismail

Comments

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Abbreviated Journal Title

Proc. Amer. Math. Soc.

Keywords

ORTHOGONAL POLYNOMIALS; FREUD POLYNOMIALS; Mathematics, Applied; Mathematics

Abstract

We revisit the ladder operators for orthogonal polynomials and re-interpret two supplementary conditions as compatibility conditions of two linear over-determined systems; one involves the variation of the polynomials with respect to the variable z ( spectral parameter) and the other a recurrence relation in n ( the lattice variable). For the Jacobi weight w(x) = (1-x)(alpha) (1+x)beta, x is an element of [-1, 1], we show how to use the compatibility conditions to explicitly determine the recurrence coefficients of the monic Jacobi polynomials.

Journal Title

Proceedings of the American Mathematical Society

Volume

133

Issue/Number

2

Publication Date

1-1-2005

Document Type

Article

Language

English

First Page

465

Last Page

472

WOS Identifier

WOS:000224695400020

ISSN

0002-9939

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