Communication Evaluation of the Remainders of a Class of Series by Using Saddle-Point Method

Remainders of various forms of series expressions of a function
$F(x)$
, which arises frequently in the high-frequency solutions of electromagnetic wave radiation and scattering problems, are transformed into some integrals. Then, the saddle-point method is applied to those integrals to obtain accurate approximations for terminating the series expressions. The accuracy improvements are illustrated by numerical examples and graphs.