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Alternate forms of the associated Legendre functions for use in geomagnetic modeling.

Journal of Geomagnetism & Geoelectricity

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Abstract

An inconvenience attending traditional use of associated Legendre functions in global modeling is that the functions are not separable with respect to the 2 indices (order and degree). In 1973 Merilees suggested a way to avoid the problem by showing that associated Legendre functions of order m and degree m+k can be expressed in terms of elementary functions. This note calls attention to some possible gains in time savings and accuracy in geomagnetic modeling based upon this form. For this purpose, expansions of associated Legendre polynomials in terms of sines and cosines of multiple angles are displayed up to degree and order 10. Examples are also given explaining how some surface spherical harmonics can be transformed into true Fourier series for selected polar great circle paths. -from Authors

Additional Publication Details

Publication type:
Article
Publication Subtype:
Journal Article
Title:
Alternate forms of the associated Legendre functions for use in geomagnetic modeling.
Series title:
Journal of Geomagnetism & Geoelectricity
Volume
38
Issue:
6
Year Published:
1986
Language:
English
Larger Work Type:
Article
Larger Work Subtype:
Journal Article
Larger Work Title:
Journal of Geomagnetism & Geoelectricity
First page:
599
Last page:
609
Number of Pages:
11