Applications of approximate expressions for complete elliptic integrals

Abstract Engineering problems involving complete elliptic integrals are tedious to handle even if a closed form solution is available. Most tables for elliptic integrals advance in 1 degree of the modulus, thus making accurate interpolation difficult. If the equation contains the modulus p of the elliptic integral as well as the integral itself a solution of the unknown modulus can become very lengthy. A rational expression is proposed here for K(p) and E(p) instead of a transcendental one, reducing the solution to an explicit form or, at least, to an algebraic equation.