This monograph summarizes the special functions needed in the performance analysis of wireless communications systems.On the basis of special Gaussian and Owen functions, the methodology for the calculation of the relationship for symbol and bit error probabilities with coherent reception, for the two-dimensional multi-positional signal constructions in communications channel with deterministic parameters and additive white Gaussian noise (AWGN), was developed. To explain the concepts, examples are provided after the mathematical proofs to illustrate how the theorems could be applied; this includes symbol and bit error probability formulas receiving for present signal constructions (QAM, PSK, APSK and HEX), and error probability dependencies from signal-to-noise ratio (SNR).There are many books in communications theory dealing with several topics covered in this monograph, but none has consolidated all error probability calculations in a single book. This book therefore serves a very niche area.This text is written for graduate students, researchers, and professionals specializing in wireless communications and electrical engineering; dealing with probability and statistics, approximation, and analysis & differential equations.