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Generating functions and semi-classical orthogonal polynomials

Published online by Cambridge University Press:  14 November 2011

Pascal Maroni  and
Jeannette Van Iseghem
Pascal Maroni
Affiliation:
Laboratoire d'Analyse Numérique, Université P. et M. Curie, 75252 Paris cedex 05, France
Jeannette Van Iseghem
Affiliation:
UFR de Math, Université de Lille, 59655 Villeneuve d'Ascq cedex, France
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Extract

An orthogonal family of polynomials is given, and a link is made between the special form of the coefficients of their recurrence relation and a first-order linear homogenous partial differential equation satisfied by the associated generating function. A study is also made of the semiclassical character of such families.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 124 , Issue 5 , 1994 , pp. 1003 - 1011
Copyright
Copyright © Royal Society of Edinburgh 1994

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References

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