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Some integral equations involving finite parts of divergent integrals

Published online by Cambridge University Press:  18 May 2009

A. Erdélyi
A. Erdélyi
Affiliation:
Mathematical Institute of the University, 20Chambers Street, Edinburgh, 1.
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In recent years, a number of special integral equations of the first kind was discussed by several authors (see [l]–[4], [6], [7], [9]–[18]). The kernels of these integral equations are special functions of the hypergeometric family, and it was necessary to restrict the parameters appearing in these functions to secure convergence of the integrals. If these restrictions are removed, the integral fails to converge but it may possess a finite part (in Hadamard's sense), and the question arises whether the methods used in the restricted case will alsoapply in the new situation. Indeed, one could pose the moregeneral problem of Volterra integral equations involving finite parts of divergent integrals [19]

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 8 , Issue 1 , January 1967 , pp. 50 - 54
Copyright
Copyright © Glasgow Mathematical Journal Trust 1967

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