Natural basis expansion of functions of the distance between two points: Generalization of Laplace's and Neumann's expansions
- 1 January 1974
- journal article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 15 (1) , 114-118
- https://doi.org/10.1063/1.1666487
Abstract
A method of obtaining expansions of functions of r12 utilizing solutions of separable differential operators which annihilate the functions is presented. Expansions of r12 n in spherical polar and confocal elliptic coordinates are obtained in terms of solutions of a generalized Laplace operator.Keywords
This publication has 2 references indexed in Scilit:
- Generalization of Laplace's Expansion to Arbitrary Powers and Functions of the Distance between Two PointsJournal of Mathematical Physics, 1964
- Entwickelung der in elliptischen Coordinaten ausgedrückten reciproken Entfernung zweier Puncte in Reihen, welche nach den Laplace'schen Y(n) fortschreiten; und Anwendung dieser Reihen zur Bestimmung des magnetischen Zustandes eines Rotations-Ellipsoids, welcher durch vertheilende Kräfte erregt ist.Journal für die reine und angewandte Mathematik (Crelles Journal), 1848