The Mysterious Behavior of Term by Term Expectation

Generalizing detection performance expressions by incorporating new fading models such as Weibul and generalized Gamma （α-μ） can be accomplished at the expense of mathematical complexity. Non-integer powers combined with exponential or special functions represent a real challenge in evaluating the necessary integrals. In this paper the authors highlight the divergence problems associated with solving complicated integrals by series expansions focusing on detection problems and illustrating the common mistakes encountered when carrying term by term integration. Additionally, the authors collected different mathematical theories to consolidate the sufficient conditions to achieve convergent results.