The probability of detection of N integrated incoherently received signal samples of constant received signal-to-noise ratio, X, with a normalized detection threshold, Y, is presented. Other expressions which are less reliable, and less accurate for \(P_ N(X,Y)\) are discussed. Computation of \(P_ N(X,Y)\) employing two criteria, absolute error and relative error, on a VAX/ll computer with double precision calculations is achieved. The underflow region run times and many algorithms with resulting programs based on computer-free notation are given. The function \(P_ N(X,Y)\) can be equated to the generalized Marcum Q- functions \(Q_ m(\alpha,\beta)\) by \(P_ N(X,Y)=Q_ m(\sqrt{2NX},\sqrt{2Y})\). The calculation of the normalized threshold value and modified expressions are given in an appendix.