Improved Numerical Evaluation Method for Elliptic Integrals

Abstract

Two modifications to Bartky's method for numerical evaluation of complete elliptic integrals increase rate of convergence and eliminate loss of accuracy due to roundoff errors. Other integrals (nonelliptic) evaluated by manipulating integrand into form F(R)/R required for evaluation by this method. Improved method used to map upper half of complex plane conformally onto interior or exterior of round-nosed wedges of various angles.