Abstract
We propose two kinds of novel formulas for calculating the toroidal function (TF) of the second kind. The first formula, which is applicable to the TF of low degree, has the superior performance with respect to computation time (about 0.5 ms on a 486SX based PC). The second has been formulated by using the technique of Landen's transformation for complete elliptic integrals. We confirmed on the same machine that TF of degree 50 can be calculated by the our second formula in the reasonable computation time. Proposed formulas will apply to the numerical computation of electric fields.
