Summary
General recurrence relations between the coefficients in thenth and (n+1)th order spherical harmonic multipole expansions are derived. The particular application presented here is the derivation of the equations concerned with representing the geomagnetic field by magnetic multipoles. The equations up to the 3rd order multipole are given as an example of the method. The main advantage in using these recurrence relations rather than other methods is that the mathematics is reduced to merely a matter of successive substitutions and this allows a fast step by step generation of the required equations, in a form for which there is a simple numerical program for solution.
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References
S. Chapman andJ. Bartels,Geomagnetism II (Oxford 1951), § 17.4.
A. Schuster,Diurnal Variation of Terrestrial Magnetism, Phil. Trans. Roy. Soc. London [A]208 (1908), 163.
D. E. Winch andL. Slaucitajs,Geomagnetic Multipoles 1829–1960, Pure and Applied Geophysics63, (1966), 22.
D. E. Winch andL. Slaucitajs,Geomagnetic Multipoles, 1965.0, Pure and Applied Geophysics66 (1967), 1.
D. E. Winch,The Fourth Order Geomagnetic Multipole: The Sedecimupole, Pure and Applied Geophysics67 (1967), 112.
E. W. Hobson,Theory of Spherical and Ellipsoidal Harmonics (Chelsea N.Y., 1955), 131.
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James, R.W. On recurrence relations for multipole coefficients. PAGEOPH 68, 83–89 (1967). https://doi.org/10.1007/BF00874886
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DOI: https://doi.org/10.1007/BF00874886