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Continued fraction solutions of the Riccati equation

Published online by Cambridge University Press:  17 April 2009

A.N. Stokes
A.N. Stokes
Affiliation:
Division of Mathematics and Statistics, CSIRO, PO Box 310, South Melbourne, Victoria 3205, Australia.
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Abstract

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It is shown that for a solution of a Riccati equation with polynomial coefficients an expansion can be constructed as a Stieltjes continued fraction, with coefficients given by a recurrence relation, which is in general non-linear. Particular expansions associated with hypergeometric and confluent hypergeometric equations are given, and are shown to have a uniquely simple form.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 25 , Issue 2 , April 1982 , pp. 207 - 214
Copyright
Copyright © Australian Mathematical Society 1982

References

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