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The solution of certain triple integral equations involving inverse Mellin transforms†

J. Tweed
1973 Glasgow Mathematical Journal  
1. Introduction. In this paper, we shall be concerned with the solution of triple integral equations of the type Ji~ '[(1 +s)"M(s); /•] = 0 M ~1 [cot (ns/n)i4(s); r] = /(/•) (0 < r < a), (a < r < b), (b<r< oo), (1.1) where M ' is the inverse Mellin transform, n is a positive integer, and -1 < Re5 < 0. The use of these equations will be illustrated by their application to two well-known problems in the mathematical theory of elasticity and further applications will be reported later. We begin by
more » ... later. We begin by considering the equations J?-1 [(\+sy l A(s);r~\=0 J/-l [cot(ns)A(s);r]=f(r) where -1 < Re s < 0. The method of solution is similar to that used by Lowengrub and Srivastava [1] for the solution of triple integral equations with trigonometric kernels and involves the assumption of a solution of the form (2.2) where p(t) is an unknown function to be determined later. It is clear that, with this choice ofA(s), = and therefore, since
doi:10.1017/s0017089500001749 fatcat:tq53gy7anvcbdivbcufivstsvi