NIST logo

Publication Citation: Eigenfunction expansions for a fundamental solution of Laplace's equation on R3 in parabolic and elliptic cylinder coordinates

NIST Authors in Bold

Author(s): Howard S. Cohl; Hans Volkmer;
Title: Eigenfunction expansions for a fundamental solution of Laplace's equation on R3 in parabolic and elliptic cylinder coordinates
Published: August 14, 2012
Abstract: A fundamental solution of Laplace's equation in three dimensions is expanded in harmonic functions that are separated in parabolic or elliptic cylinder coordinates. There are two expansions in each case which reduce to expansions of the Bessel functions J0(kr) or K0(kr), r2 = (x-x0)2+(y-y0)2, in parabolic and elliptic cylinder functions. Advantage is taken of the fact that K0(kr) is a fundamental solution and J0(kr) is the Riemann function of partial differential equations on the Euclidean plane.
Citation: Journal of Physics A: Mathematical and Theoretical
Volume: 45
Pages: 20 pp.
Keywords: Fundamental solution; Laplace equation; Parabolic cylinder coordinates; Elliptic cylinder coordinates; Parabolic cylinder harmonics; Confluent hypergeometric functions; Mathieu functions
Research Areas: Modeling
DOI: http://dx.doi.org/10.1088/1751-8113/45/35/355204  (Note: May link to a non-U.S. Government webpage)
PDF version: PDF Document Click here to retrieve PDF version of paper (722KB)