Geodesic
Dual integral equations with trigonometrical kernels†
Glasgow mathematical journal, Tome 5 (1962) no. 3, pp. 147-152

Voir la notice de l'article provenant de la source Cambridge University Press

In the analysis of mixed boundary value problems in the plane, we encounter dual integral equations of the typeIf we make the substitutions cos we obtain a pair of dual integral equations of the Titchmarsh type [1, p. 334] with α = − 1, v = − 1⁄2 (in Titchmarsh's notation). This is a particular case which is not covered by Busbridge's general solution [2], so that special methods have to be derived for the solution. 
Sneddon, Ian N. Dual integral equations with trigonometrical kernels†. Glasgow mathematical journal, Tome 5 (1962) no. 3, pp. 147-152. doi: 10.1017/S2040618500034481
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[1] 1.Titchmarsh, E. C., Introduction to the theory of Fourier integrals (Clarendon Press, Oxford, 1937). Google Scholar

[2] 2.Busbridge, I. W., Dual integral equations, Proc. London Math. Soc. 44 (1938), 115–129. Google Scholar | DOI

[3] 3.Chong, F., Solution by dual integral equations of a plane strain Boussinesq problem for an orthotropic medium, Iowa State Coll. Jour, of Sci. 27 (1953), 321–334. Google Scholar

[4] 4.Fredricks, R. W., Solution of a pair of integral equations from electrostatics, Proc. Nat. Acad. Sci. 44 (1958), 309–312. Google Scholar | DOI

[5] 5.Watson, G. N., A treatise on the theory of Bessel functions, 2nd edn, (Cambridge Univ. Press, 1944). Google Scholar

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