Recurrence relations for spherical waves
Article first published online: 7 DEC 2012
Copyright 1996 by the American Geophysical Union.
Volume 31, Issue 6, pages 1743–1748, November-December 1996
How to Cite
1996), Recurrence relations for spherical waves, Radio Sci., 31(6), 1743–1748, doi:10.1029/96RS02790.(
- Issue published online: 7 DEC 2012
- Article first published online: 7 DEC 2012
- Manuscript Accepted: 6 SEP 1996
- Manuscript Received: 27 SEP 1995
This paper derives new recurrence relations for scalar spherical waves in Cartesian coordinates and compares the performance of these relations with that of traditional recurrence relations. They are numerically stable for travelling waves and some standing waves, and are faster for evaluating scalar spherical waves up to order 40 on a nonspherical surface. Because of their algebraic simplicity, they will be especially useful for symbolic-algebra computer programs, allowing explicit expressions for scalar and vector spherical waves to be obtained using a succinct procedure.