Numerical calculation of elliptic integrals and elliptic functions. III

Summary This paper is a continuation of 2, 3]. It contains anALGOL program for the incomplete elliptic integral of the third kind based on a theory described in 4]. This program replaces the inadequate one based on the Gauß-transformation which was published in 2]. In addition, anAlgol program for a general complete elliptic integral is presented. Editor's note. In this fascicle, prepublication of algorithms from the Special Functions Series of the Handbook for Automatic Computation is continued. Algorithms are published inAlgol 60 reference language as approved by the IFIP. Contributions in this series should be styled after the most recently published ones.This research was supported by the Advanced Research Projects Agency of the Department of Defense and was monitored by the U. S. Army Research Office —Durham under Contract DA-31-124-ARO-D-257.