Series Representations for Rice's Ie Function

Abstract

Two new series representations for the Rice function <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Ie (k, x)</tex> are presented. One of the series involves the modified Struve functions and the other involves the modified Bessel functions. These two series complement each other in their convergence speeds as functions of the values of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</tex> and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x</tex> . The truncation error bounds are derived for both series. Therefore, they can be used alternatively with high efficiency and known precision.