Elliptic_Integrals.​zip

Compute incomplete Legendre elliptic integrals of the first, second, and third kind.

These MATLAB functions allow the user to compute incomplete Legendre elliptic integrals of the first, second, and third kind, and symmetric elliptic integrals using vectorized versions of the duplication algorithms developed by B. C. Carlson and E. M. Notis (see Numer. Math., 33}, pp. 1-16 (1979) and ACM Trans. on Math. Software, 7(3), pp. 398-403 (1981)). User should be aware that Carlson's characteristic "n" in the Legendre elliptic integral of the third kind is minus the value that appears in "Handbook of Mathematical Functions", M. Abramowitz and I. A. Stegun, ed., Dover (1965). Computed values for the integrals have been checked against tables in this handbook, and a small test script to allow users to make their own checks is also included. The functions do not require any toolboxes or products in addition to matlab. They have been tested under Release 13, version 6.5.0.180913a.