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Jacobi polynomials from compatibility conditions
Author(s):
Yang
Chen;
Mourad
Ismail
Journal:
Proc. Amer. Math. Soc.
133
(2005),
465-472.
MSC (2000):
Primary 33C45;
Secondary 42C05
Posted:
August 30, 2004
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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:
10.1090/S0002-9939-04-07566-5
PII:
S 0002-9939(04)07566-5
Received by editor(s):
February 21, 2003
Received by editor(s) in revised form:
October 2, 2003
Posted:
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
Copyright of article:
Copyright
2004,
American Mathematical Society
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![\begin{displaymath}w(x)=(1-x)^{\alpha}(1+x)^{\beta},\qquad x\in[-1,1],\end{displaymath}](/proc/2005-133-02/S0002-9939-04-07566-5/gif-abstract0/img3.gif){kind=small}
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