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Associated Laguerre and Hermite polynomials

Published online by Cambridge University Press:  14 November 2011

Richard Askey  and
Jet Wimp
Richard Askey
Affiliation:
Mathematics Department, University of Wisconsin-Madison, Madison, Wisconsin 53706, U.S.A.
Jet Wimp
Affiliation:
Department of Mathematical Sciences, Drexel University, Philadelphia, Pennsylvania 19104, U.S.A.
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Synopsis

Explicit orthogonality relations are found for the associated Laguerre and Hermite polynomials. One consequence is the construction of the [n − 1/n] Padé approximation to Ψ(a + 1, b; x)/Ψ(a, b; x), where Ψ(a, b; x) is the second solution to the confluent hypergeometric differential equation that does not grow rapidly at infinity.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 96 , Issue 1-2 , 1984 , pp. 15 - 37
Copyright
Copyright © Royal Society of Edinburgh 1984

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