New recurrence relations for spherical harmonic functions and their derivatives

Details New recurrence relations for spherical harmonic functions and their derivatives New recurrence relations for spherical harmonic functions and their derivatives

Nov 1968

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1968pepi....1..396w&link_type=abstract

Physics of the Earth and Planetary Interiors, Volume 1, Issue 6, p. 396-400.

Physics

1

Scientific paper

A single pair of recurrence relations are presented for the rapid numerical evaluation of spherical harmonic functions Pnm (cos θ)sincos mφ and their first derivatives Xnm (cos θ) sincos mφ, Ynm (cos θ)sincos mφ, Znm (cos θ)sincos mφ which occur in spherical harmonic analyses of the Earth's main magnetic field. The same pair of recurrence relations may also be applied to the evaluation of second derivatives.

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