TY - JOUR
AU - Carslaw, H. S.
AB - THE GREEN'S FUNCTION FOR A WEDGE OF ANY ANGLE. 865 THE GREEN'S FUNCTION FOR A WEDGE OF ANY ANGLE, AND OTHER PROBLEMS IN THE CONDUCTION OF HEAT By H. S. CARSLAW. [Eeceived October 30th, 1909.—Read November 11th, 1909.—Received, in revised form, February 21st, 1910.] Introduction. In a former paper* I have obtained certain multiform solutions of the partial differential equations of conduction of heat and sound, with the period 2n7r: and I have shown how these solutions can be applied to problems in which the boundaries are planes including an angle nirjm, m and n being any integers. This work involved the use of the theory of images in a Riemann's space, and the object of the investigation was to establish the application of that theory to these physical equations. In this paper I shall give the solution for the case of a wedge of any angle, proving that this solution can be obtained without the introduction of the Riemann's space. That this is possible for the potential function was shown by Sommerfeld in his original paper, t The discussion which I give for the equation of conduction can be readily adapted to the problem of diffraction of sound. 
TI - The Green's Function for a Wedge of any Angle, and Other Problems in the Conduction of Heat
JF - Proceedings of the London Mathematical Society
DO - 10.1112/plms/s2-8.1.365
DA - 1910-01-01
UR - https://www.deepdyve.com/lp/wiley/the-green-s-function-for-a-wedge-of-any-angle-and-other-problems-in-xKj0ClYOd9
SP - 365
EP - 374
VL - s2-8
IS - 1
DP - DeepDyve
ER -