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J. A. 50 In 1914 T. J. I’A. Bromwich (1875–1929) showed how Laplace transforms51 can be used to solve the wave equation by eliminating the temporal dependence, leaving a boundary-value problem. Interestly he then solved this boundary-value problem using Green’s functions. Then, unknowingly he found as an example the Green’s function for the one-dimensional wave equation with fixed ends (see his Example 5 on page 438). A. N. Lowan (1898–1962) applied Bromwich’s idea to finding the wave motions within a wedge52 of infinite radius and an infinite solid53 which is exterior to a cylinder or sphere.

1912: Die Greensche Funktion der Schwingungsgleichung. Jahrber. Deutsch. , 21, 309–353. 74 Schot, S. , 1992: Eighty years of Sommerfeld’s radiation condition. Hist. , 19, 385–401. , 1959: Partial Differential Equations of Mathematical Physics. Cambridge, 522 pp. , Ph. Frank, H. Weber, and B. Riemann, 1925: Die Differential- und Integralgleichungen der Mechanik und Physik. Vol I. Braunschweig, F. Vieweg, 687 pp. , 1914: Belastete Integralgleichungen. Rend. Circ. Matem. Palermo, 37, 169–197. 27) where λ = λn , the eigenvalue of the system, and q > 0.

It consisted of two parts: Green’s function for a bounded and unbounded region. For a finite domain he showed that the Green’s funcline sources for the equation of conduction of heat in cylindrical coordinates by the Laplace transformation. Philos. , Ser. 7 , 31, 204–208. , 1860: Theorie der Luftschwingungen in R¨ ohren mit offenen Enden. J. Reine Angew. , 57, 1–72. , 1891: Uber ¨ die partielle Differentialgleichung ∆u + k 2 u = 0 und deren Auftreten in der mathematischer Physik . Leipzig, Teubner, 339 pp.

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