Addition theorems for spherical wave functions

Stein, Seymour

doi:10.1090/qam/120407

Author: Seymour Stein
Journal: Quart. Appl. Math. 19 (1961), 15-24
MSC: Primary 33.00
DOI: https://doi.org/10.1090/qam/120407
MathSciNet review: 120407
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Abstract: Addition theorems are described for spherical vector wave functions, under both rotations and translations of the coordinate system. These functions are the characteristic solutions in spherical coordinates of the vector wave equation, such as occurs in electromagnetic problems. The vector wave function addition theorems are based on corresponding theorems for the spherical scalar wave functions. The latter are reviewed and discussed.

William Sterling Ament, WAVE PROPAGATION IN SUSPENSIONS, ProQuest LLC, Ann Arbor, MI, 1959. Thesis (Ph.D.)–Brown University. MR 2612877

J. Stratton, Electromagnetic theory, McGraw-Hill, N. Y., 1941, p. 414 ff.

Ibid., p. 404–406

Ibid., p. 401

R. Courant and D. Hilbert, Methods of mathematical physics. Vol. I, Interscience Publishers, Inc., New York, N.Y., 1953. MR 0065391

A. Erdelyi, et al., Higher transcendental functions, vol. 2, McGraw-Hill, N. Y., 1953 Chap. 11, esp. p. 257

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Ibid., p. 24

Ibid., p. 6–8

Ibid., p. 61, Eq. 4.3.4, with ${j_1} = 1$

J. S. Lamont, Applications of finite groups, Academic Press, N. Y., 1959, p. 150–151

Reference 11, p. 61, Eq. 4.3.2. with ${j_1} = 1$

Reference 10, p. 21, in which the formulas are correct for the $U_{kl}^n$ , rather than the $H_{kl}^m$ as written; also p. 19

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Reference 11, p. 45 ff., also Eqs. 4.6.5, 3.7.5, 3.7.3, 3.6.10, 3.6.11, 3.1.5

Reference 11, p. 48–50, and p. 95