Compact extended algorithms for elliptic integrals in electromagnetic field and potential computations. II. Elliptic integral of third kind with extended integration range

Electromagnetic field and potential computations on elements with curved contours in boundary and volume integral methods (BEM, VIM) require evaluation of a number of Jacobian complete and/or incomplete elliptic integrals of all the three kinds for the same modulus but different angles depending upon the arc length and the angle coordinate of the field point. Up to now they have been evaluated individually repeating the same algorithms a number of times. To reduce such redundant computations, as in Part I for elliptic integrals of first and second kind, a new compact algorithm based on Bartky´s transformation is developed in the present paper for the elliptic integral of third kind with an extended integration range -π⩽a⩽π. Computational accuracy and time-saving are discussed