Abstract
A generalization of the spherical harmonic addition theorem is proved. The resulting polynomial with four parameters, which corresponds to the Legendre polynomial for the usual spherical harmonic addition theorem, is expressed as four different but equivalent series. Each of them is a finite series of the Gegenbauer polynomials. Thereby the symmetry properties of this polynomial are clarified.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Joos, H.: Fortschr. Physik10, 65 (1962).
Rose, M. E.: Elementary theory of angular momentum, Chap. IV, V. New York: John Wiley and Sons 1957.
Erdelyi, A.: Bateman manuscript project. Higher transcendental functions. Vol. I, p. 175. London, Toronto, New York: McGraw-Hill Book Company, Inc. 1953.
Racah, G.: Phys. Rev.62, 438 (1942).
Domokos, G.: Phys. Rev.159, 1387 (1967);Freedman, D. Z., andWang, J. M.: Phys. Rev.160, 1560 (1967).
Wigner, E. P.: Gruppentheorie und ihre Anwendung auf die Quantenmechanik der Atomspektren. Braunschweig: Friedrich Vieweg und Sohn 1931.
Titchmarsh, E. C.: Theory of functions, Section 5.81. New York: Oxford Univ. Press. 1939.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Munakata, Y. A generalization of the spherical harmonic addition theorem. Commun.Math. Phys. 9, 18–37 (1968). https://doi.org/10.1007/BF01654029
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01654029