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Spherical harmonics in a non-polar co-ordinate system and application to Fourier series in 2-sphere

✍ Scribed by H. M. Nasir


Publisher
John Wiley and Sons
Year
2007
Tongue
English
Weight
294 KB
Volume
30
Category
Article
ISSN
0170-4214

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✦ Synopsis


Abstract

A new non‐polar spherical co‐ordinate system for the three‐dimensional space is introduced. The co‐ordinate system is composed of six local co‐ordinate systems mapped from six faces of a cube on to the 2‐sphere. Weakly orthogonal and orthogonal spherical harmonics are constructed in this co‐ordinate system. The spherical harmonics are easily computable functions consisting of polynomials and square root of polynomials. Examples of finite Fourier series computations are given in terms of the new spherical harmonics to demonstrate their immediate applicability. Copyright © 2007 John Wiley & Sons, Ltd.