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Some Integral Equations Involving Hypergeometric Functions

Published online by Cambridge University Press:  20 January 2009

E. R. Love
E. R. Love
Affiliation:
University of Edinburgh and University of Melbourne
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Summary

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An integral equation of the first kind, with kernel involving a hypergeometric function, is discussed. Conditions sufficient for uniqueness of solutions are given, then conditions necessary for existence of solutions. Conditions sufficient for existence of solutions, only a little stricter than the necessary conditions, are given; and with them two distinct forms of explicit solution. These two forms are associated at first with different ranges of the parameters, but their validity in the complementary ranges is also discussed. Before giving the existence theory a digression is made on a subsidiary integral equation.

Corresponding theorems for another integral equation resembling the main one are deduced from some of the previous theorems. Two more equations of similar form, less closely related, will be considered in another paper. Special cases of some of these four integral equations have been considered recently by Erdélyi, Higgins, Wimp and others.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 15 , Issue 3 , June 1967 , pp. 169 - 198
Copyright
Copyright © Edinburgh Mathematical Society 1967

References

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