A third order iterative procedure for computing exact confidence limits for Poisson expectation values

The calculation of exact confidence limits for the expectation value of a Poisson distribution when a single observation of K events is given by means of a second order iterative algorithm was recently presented. Here it is shown that the structure of the equations to be solved admits the use of a third order algorithm, thereby significantly reducing computation time, especially for pocket calculators, with practically no additional computational effort.