Geodesic
A note on integral equations
Glasgow mathematical journal, Tome 13 (1972) no. 2, pp. 119-121

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In a recent paper Cooke [1] obtained a solution of the integral equationby using the identityand the technique, first used by Copson, of interchanging the orders of integration and hence reducing the problem to that of the successive solution of two Abel integral equations. It is also shown in [1] that the above identity can also be used to solve the dual series equationsThe kernel in equation (1) is a particular member of a general class of kernels which the author [6] has shown to be such that the resulting integral equation is directly soluble by using Copson's technique. The particular example of equation (1) is given in [6] and the identity of equation (2) was used by the author [7] to obtain the solution of equation (3). 
Williams, W. E. A note on integral equations. Glasgow mathematical journal, Tome 13 (1972) no. 2, pp. 119-121. doi: 10.1017/S0017089500001518
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[1] 1.Cooke, J. C., The solution of some integral equations and their connection with dual integral equations and series, Glasgow Math. J. 11 (1970), 9–20. Google Scholar | DOI

[2] 2.Lundgren, T. and Chiang, D., Solution of a class of singular integral equations, Quart. Appl. Math. 24 (1967), 303–313. Google Scholar | DOI

[3] 3.Peters, A. S., A note on the integral equation of the first kind with a Cauchy kernel, Comm. Pure App. Math. 16 (1963), 57–61. Google Scholar | DOI

[4] 4.Peters, A. S., Abel's equation and the Cauchy integral equation of the second kind, Comm. Pure App. Math. 21 (1968), 51–65. Google Scholar | DOI

[5] 5.Peters, A. S., Some integral equations related to Abel's equation and the Hilbert transform, Comm. Pure App. Math. 22 (1969), 539–560. Google Scholar | DOI

[6] 6.Williams, W. E., A class of integral equations, Proc. Cambridge Philos. Soc. 59 (1963), 589–597. Google Scholar | DOI

[7] 7.Williams, W. E., The solution of dual series and dual integral equations, Proc. Glasgow Math. Assoc. 6 (1964), 123–129. Google Scholar | DOI

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