Jacobi polynomials from compatibility conditions
Authors:
Yang Chen and Mourad Ismail
Journal:
Proc. Amer. Math. Soc. 133 (2005), 465472
MSC (2000):
Primary 33C45; Secondary 42C05
Published electronically:
August 30, 2004
MathSciNet review:
2093069
Fulltext PDF Free Access
Abstract 
References 
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Abstract: We revisit the ladder operators for orthogonal polynomials and reinterpret two supplementary conditions as compatibility conditions of two linear overdetermined 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:
http://dx.doi.org/10.1090/S0002993904075665
PII:
S 00029939(04)075665
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 9970865 and by EPSRC grant GR/S14108.
Communicated by:
David R. Larson
Article copyright:
© Copyright 2004
American Mathematical Society
