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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)


Recent investigations of the separation of Laplace's equation

Authors: Parry Moon and Domina Eberle Spencer
Journal: Proc. Amer. Math. Soc. 4 (1953), 302-307
MSC: Primary 36.0X
MathSciNet review: 0053335
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  • [1] Parry Moon and Domina Eberle Spencer, Theorems on separability in Riemannian 𝑛-space, Proc. Amer. Math. Soc. 3 (1952), 635–642. MR 0049439 (14,173h),
  • [2] N. Levinson, B. Bogert, and R. M. Redheffer, Separation of Laplace’s equation, Quart. Appl. Math. 7 (1949), 241–262. MR 0032091 (11,251f)
  • [3] R. M. Redheffer, Separation of Laplace's equation (Massachusetts Institute of Technology Ph.D. Thesis, 1948); Research Laboratory of Electronics, M.I.T., Technical Report no. 68, June 2, 1948.
  • [4] Luther Pfahler Eisenhart, Separable systems of Stackel, Ann. of Math. (2) 35 (1934), no. 2, 284–305. MR 1503163,
  • [5] G. Lamé, Leçons sur les coordonnées curvilignes et leurs diverses applications, Paris, 1859.
  • [6] M. Bôcher, Über die Reihenentwickelungen der Potentialtheorie, Leipzig, Teubner, 1894. (See particularly the list of separable cyclide systems on p. 102 and the pictures on pp. 72 to 85); C. Segre, Etude des différentes surfaces du 4$ ^{e}$ ordre à conique double ou cuspidale, Math. Ann. vol. 24 (1884) p. 313.
  • [7] A. Wangerin, Reduction der Potentialgleichung für gewisse Rotationskörper auf eine gewöhnliche Differentialgleichung, Preis. d. Jablonowski Ges., Leipzig, no. 18, 1875; Über ein dreifach orthogonales Flächensystem, gebildet aus gewissen Flächen vierter Ordnung, J. Reine Angew. Math. vol. 82 (1877) pp. 145, 348; Über die Reduction der Gleichung (Laplace) auf gewöhnliche Differentialgleichungen, Monatsber. Kön. Akad. d. Wissen. Berlin, 1878, p. 152.
  • [8] G. Darboux, Sur l'application des méthodes de la physique mathématique à l'étude des corps terminés par des cyclides, C. R. Acad. Sci. Paris vol. 83 (1876) pp. 1037, 1099; vol. 84 (1877) p. 298.
  • [9] R. M. Redheffer, Tech. Report No. 68, p. 60.
  • [10] Parry Moon and Domina Eberle Spencer, Separability in a class of coordinate systems, J. Franklin Inst. 254 (1952), 227–242. MR 0049438 (14,173g)

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PII: S 0002-9939(1953)0053335-X
Article copyright: © Copyright 1953 American Mathematical Society

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