Fourier transform summation of Legendre series and D-functions |
| |
| Authors: | T Risbo |
| |
| Institution: | (1) Geophysical Department, Niels Bohr Institute of Astronomy, Physics and Geophysics, Haraldsgade 6, DK-2200 Copenhagen, Denmark |
| |
| Abstract: | The relation between D- and d-functions, spherical harmonic functions and Legendre functions is reviewed. Dmatrices and irreducible representations of the rotation group O(3) and SU(2) group are briefly reviewed. Two new recursive methods for calculations of D-matrices are presented. Legendre functions are evaluated as part of this scheme. Vector spherical harmonics in the form af generalized spherical harmonics are also included as well as derivatives of the spherical harmonics. The special dmatrices evaluated for argument equal to /2 offer a simple method of calculating the Fourier coefficients of Legendre functions, derivatives of Legendre functions and vector spherical harmonics. Summation of a Legendre series or a full synthesis on the unit sphere of a field can then be performed by transforming the spherical harmonic coefficients to Fourier coefficients and making the summation by an inverse FFT (Fast Fourier Transform). The procedure is general and can also be applied to evaluate derivatives of a field and components of vector and tensor fields. |
| |
| Keywords: | Legendre functions Spherical harmonics Vector spherical harmonics D-functions |
| 本文献已被 SpringerLink 等数据库收录！ |
|
