, Volume 10, Issue 1, pp 13-26

Numerical computation of real or complex elliptic integrals

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Abstract

Algorithms for numerical computation of symmetric elliptic integrals of all three kinds are improved in several ways and extended to complex values of the variables (with some restrictions in the case of the integral of the third kind). Numerical check values, consistency checks, and relations to Legendre's integrals and Bulirsch's integrals are included.

This work was supported by the Director of Energy Research, Office of Basic Energy Sciences. The Ames Laboratory is operated for the US Department of Energy by Iowa State University under Contract W-7405-ENG-82.