Abstract
A single pair of recurrence relations are presented for the rapid numerical evaluation of spherical harmonic functions P n m (cos θ) sin cos mφ and their first derivatives X n m (cos θ) sin cos mφ, Y n m (cos θ) sin cos mφ, Z n m (cos θ) sin cos 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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