## Generalized little $q$-Jacobi polynomials as eigensolutions of higher-order $q$-difference operators

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- by Luc Vinet and Alexei Zhedanov PDF
- Proc. Amer. Math. Soc.
**129**(2001), 1317-1327 Request permission

## Abstract:

We consider the polynomials $p_n(x;a,b;M)$ obtained from the little $q$-Jacobi polynomials $p_n(x;a, b)$ by inserting a discrete mass $M$ at $x=0$ in the orthogonality measure. We show that for $a=q^j, \; j=0,1,2,\dots$, the polynomials $p_n(x;a,b;M)$ are eigensolutions of a linear $q$-difference operator of order $2j+4$ with polynomial coefficients. This provides a $q$-analog of results recently obtained for the Krall polynomials.## References

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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 Centre-ville, Montréal, Québec, Canada H3C 3J7
- MR Author ID: 178665
- ORCID: 0000-0001-6211-7907
- Email: vinet@crm.umontreal.ca
**Alexei Zhedanov**- Affiliation: Donetsk Institute for Physics and Technology, Donetsk 340114, Ukraine
- MR Author ID: 234560
- Email: zhedanov@kinetic.ac.donetsk.ua
- 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, INTAS-96-0700 grant and project 96-01-00281 supported by RFBR (Russia). The second author thanks Centre de recherches mathématiques of the Université de Montréal for hospitality.
- Communicated by: Hal L. Smith
- © Copyright 2001 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**129**(2001), 1317-1327 - MSC (2000): Primary 33D45
- DOI: https://doi.org/10.1090/S0002-9939-01-06047-6
- MathSciNet review: 1814158