Hansen's Method Applied to the Inversion of the Incomplete Gamma Function, with Applications

Hansen's method for obtaining the threshold for a speciried false alarm probability following noncoherent integration after square law detection is applied to finding the inverse of the incomplete gamma function. The method is algebraic and direct, circumventing the necessity for repeated evaluation of an integral or of a finite series. The method is applied to finding any specified percentile of the chi-square distribution and to finding the required signal-to-noise ratio for a specified detection probability of a Swerling II target.