Single integral representations of certain integer powers of the Gaussian Q-function and their application

Representations of the third and fourth powers of the Gaussian Q-function as a single integral with finite limits and an integrand that is Gaussian in the argument of the function are found. These representations are of the same form previously found for the first and second powers of the Q-function and, therefore, allow extended application of the moment-generating function approach for evaluating the performance of digital communication systems over generalized fading channels.