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In the scalar Helmholtz equation the variables are separated in 11 physically
interesting coordinate systems [55],
however for the vector field containing 3 scalar functions,
the complete separation of variables is possible only in 6 systems:
Cartesian, 3 cylindrical, conical and spherical ones ([55], Ch.13).
Therefore, the formal solution suggested in 1927 by F. Moeglich [368]
for the spheroidal coordinates was practically usefulness until
the work of Sh. Asano and G. Yamamoto in 1975 [141]
where the method of separation of variables was adapted for
numerical calculations by cutting the infinite linked (only partly
separated) systems of equations
(in earlier papers [432,433] one considers either scalar scattering,
or the axial incidence of the electromagnetic wave).
In 1980-1983 V.G. Farafonov [87,88,93]
improved the method of Asano-Yamamoto by use of an original
scheme of separation of the fields in two types with the invariant angular
parts [27].
At the moment the use of both approaches gave large volume of data
on the light scattering by spheroidal particles
[13,14,15,16,17,89,90,91,92,138,139,140,141,297,323,413,430].
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