Abstract
On the basis of an approximate relation, the Mie series are replaced by new ones, which can be summed exactly with the aid of various modified and generalized forms of the addition theorem for cylindrical functions. The sums obtained simultaneously simplify the initial expressions for the scattering characteristics and preserve their analytical nature. The conventional approximations for the amplitude functions and the efficiency factors rigorously follow from the new approaches if the optical parameters are properly restricted. The acceptable domains of these approaches contain the long wavelength region and are extensive enough to study the various (including inverse) scattering problems for the real disperse systems, in which the particles are suspended in a medium with similar optical properties.
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