Expressions to compute the coefficients g m n in the generalized Lorenz-Mie theory using finite series

In the framework of the generalized Lorenz-Mie theory with arbitrary location of the scatter center, the expressions to compute the properties of the scattered light involve two series of coefficients g m n,TM and g m n,TE (n from 1 to infinity , m from -n to +n). Up to now, these coefficients have been expressed as quadratures of very oscillating functions which are time-consuming and costly to perform. The authors establish new expressions permitting one to evaluate the coefficients of g m n as finite series.