Generalized little Jacobi polynomials as eigensolutions of higherorder difference operators
Authors:
Luc Vinet and Alexei Zhedanov
Journal:
Proc. Amer. Math. Soc. 129 (2001), 13171327
MSC (2000):
Primary 33D45
Published electronically:
January 8, 2001
MathSciNet review:
1814158
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Abstract: We consider the polynomials obtained from the little Jacobi polynomials by inserting a discrete mass at in the orthogonality measure. We show that for , the polynomials are eigensolutions of a linear difference operator of order with polynomial coefficients. This provides a analog of results recently obtained for the Krall polynomials.
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Additional Information
Luc Vinet
Affiliation:
Department of Mathematics and Statistics and Department of Physics, McGill University, 845 Sherbrooke St. W., Montreal, Québec, Canada H3A 2T5 – Centre de Recherches Mathématiques, Université de Montréal, C.P. 6128, succursale Centreville, Montréal, Québec, Canada H3C 3J7
Email:
vinet@crm.umontreal.ca
Alexei Zhedanov
Affiliation:
Donetsk Institute for Physics and Technology, Donetsk 340114, Ukraine
Email:
zhedanov@kinetic.ac.donetsk.ua
DOI:
http://dx.doi.org/10.1090/S0002993901060476
PII:
S 00029939(01)060476
Keywords:
Krall's polynomials,
little $q$Jacobi polynomials
Received by editor(s):
December 11, 1998
Published electronically:
January 8, 2001
Additional Notes:
The work of the first author was supported in part through funds provided by NSERC (Canada) and FCAR (Quebec). The work of the second author was supported in part through funds provided by SCST (Ukraine) Project #2.4/197, INTAS960700 grant and project 960100281 supported by RFBR (Russia). The second author thanks Centre de recherches mathématiques of the Université de Montréal for hospitality.
Communicated by:
Hal L. Smith
Article copyright:
© Copyright 2001 American Mathematical Society
