Jacobi polynomials from compatibility conditions

Authors:
Yang Chen and Mourad Ismail

Journal:
Proc. Amer. Math. Soc. **133** (2005), 465-472

MSC (2000):
Primary 33C45; Secondary 42C05

DOI:
https://doi.org/10.1090/S0002-9939-04-07566-5

Published electronically:
August 30, 2004

MathSciNet review:
2093069

Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 (spectral parameter) and the other a recurrence relation in (the lattice variable). For the Jacobi weight

we show how to use the compatibility conditions to explicitly determine the recurrence coefficients of the monic Jacobi polynomials.

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Additional Information

**Yang Chen**

Affiliation:
Department of Mathematics, Imperial College, 180 Queen’s Gate, London SW7 2BZ, United Kingdom

Email:
y.chen@imperial.ac.uk

**Mourad Ismail**

Affiliation:
Department of Mathematics, University of Central Florida, Orlando, Florida 32816

Email:
ismail@math.ucf.edu

DOI:
https://doi.org/10.1090/S0002-9939-04-07566-5

Received by editor(s):
February 21, 2003

Received by editor(s) in revised form:
October 2, 2003

Published electronically:
August 30, 2004

Additional Notes:
This research was supported by NSF grant DMS 99-70865 and by EPSRC grant GR/S14108.

Communicated by:
David R. Larson

Article copyright:
© Copyright 2004
American Mathematical Society