Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Generating functions for relatives of classical polynomials


Authors: P. D. Barry and D. J. Hurley
Journal: Proc. Amer. Math. Soc. 103 (1988), 839-846
MSC: Primary 33A99; Secondary 05A15
DOI: https://doi.org/10.1090/S0002-9939-1988-0947668-3
MathSciNet review: 947668
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: For several classical polynomials $ {u_n}(x)$ satisfying a second order linear differential equation $ {D_n}(x)$, there is a generating function $ u(x,t) = \sum\nolimits_{n = 0}^\infty {{u_n}(x){t^n}} $. We provide expansions $ \upsilon (x,t) = \sum\nolimits_{n = 0}^\infty {{\upsilon _n}(x){t^n}} $ where $ {\upsilon _n}(x)$ is a second solution of $ {D_n}(x)$.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 33A99, 05A15

Retrieve articles in all journals with MSC: 33A99, 05A15


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1988-0947668-3
Keywords: Generating functions, classical polynomials, orthogonal polynomials
Article copyright: © Copyright 1988 American Mathematical Society