Generalized Burchnall-Type Identities for Orthogonal Polynomials and Expansions

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2018
• ISSN: 1815-0659
• Main Authors: Ismail, M.E.H., Koelink, E., Román, P.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2018
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/209778
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Generalized Burchnall-Type Identities for Orthogonal Polynomials and Expansions / M.E.H. Ismail, E. Koelink, P. Román // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 27 назв. — англ.

Burchnall's method to invert the Feldheim-Watson linearization formula for the Hermite polynomials is extended to all polynomial families in the Askey-scheme and its q-analogue. The resulting expansion formulas are made explicit for several families corresponding to measures with infinite suppo...