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On Liouville's extension of Abel's integral equation

Published online by Cambridge University Press:  26 February 2010

L. S. Bosanquet
L. S. Bosanquet
Affiliation:
University College, London
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Extract

Necessary and sufficient conditions for Abel's integral equation to have a solution have been given by Tamarkin [18]. The form of the solution was obtained by Abel [1]. The corresponding integral equation for an infinite range of integration was introduced by Liouville [12], who found a solution in a restricted class of cases. In the present paper, we find necessary and sufficient conditions for Liouville's equation to have a solution, and also give the form of the solution.

Type
Research Article
Information
Mathematika , Volume 16 , Issue 1 , June 1969 , pp. 59 - 85
Copyright
Copyright © University College London 1969

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