On Certain Dual Integral Equations
Glasgow mathematical journal, Tome 5 (1961) no. 1, pp. 21-24
Voir la notice de l'article provenant de la source Cambridge University Press
In his book on Fourier Integrals, Titchmarsh [l] gave the solution of the dual integral equationsfor the case α > 0, by some difficult analysis involving the theory of Mellin transforms. Sneddon [2] has recently shown that, in the cases v = 0, α = ±1⁄2, the problem can be reduced to an Abel integral equation by making the substitutionorIt is the purpose of this note to show that the general case can be dealt with just as simply by puttingThe analysis is formal: no attempt is made to supply details of rigour.
Copson, E. T. On Certain Dual Integral Equations. Glasgow mathematical journal, Tome 5 (1961) no. 1, pp. 21-24. doi: 10.1017/S2040618500034249
@article{10_1017_S2040618500034249,
author = {Copson, E. T.},
title = {On {Certain} {Dual} {Integral} {Equations}},
journal = {Glasgow mathematical journal},
pages = {21--24},
year = {1961},
volume = {5},
number = {1},
doi = {10.1017/S2040618500034249},
url = {http://geodesic.mathdoc.fr/articles/10.1017/S2040618500034249/}
}
[1] 1.Titchmarsh, E. C., Introduction to the theory of Fourier integrals (Clarendon Press, Oxford, 1937), pp. 334–339. Google Scholar
[2] 2.Sneddon, I. N., The elementary solution of dual integral equations, Proc. Glasgow Math. Assoc., 4 (1960), 108–110. Google Scholar | DOI
[3] 3.Watson, G. N., A treatise on the theory of Bessel functions (University Press, Cambridge, 1944), p. 401, equations (1) and (3). Google Scholar
[4] 4.Whittaker, E. T. and Watson, G. N., A course of modern analysis (University Press, Cambridge, 1920), p. 229. Google Scholar
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