Uniform Asymptotic Expansions for Saddle Point Integrals - Application to a Probability Distribution Occurring in Noise Theory

This paper deals with the problem of obtaining asymptotic series for the complex integral (1) when x becomes large. Problems of this sort are quite often encountered in applied mathematics, particularly in wave propagation. T h e material presented here grew out of some recent work by G. H. Robertson 1 on the " M a r c u m Q-Function." This function, which appears in the study of radar interference, gives the distribution of the random variable (noncentral x 2 ) X z = (l/.r) X) Vn · 1971 (2)