On the use of an exponential function in approximation of elliptic integrals

Abstract

In the previous papers[1]–[3], nonlinear continuous functions could be well simulated by nonlinear resistance. Its mathematical basis came from the applicability of the fractional power approximation. From a view of using transistor-junction characteristics, the use of exponential functions will make it possible to have closed relations between given functions and transistor-junction characteristics. Hereby, in simulation of special functions, especially, of elliptic integrals, a form of approximation containing an exponential function is proposed, so that F(x, α) E (x, α) Π (x, α, n) ⋍ c 0+c 1x+c 2e px , where F(x, α), E(x, α) and Π(x, α, n) are elliptic integrals of the first, second and third kinds in the Legendre's canonical form with their modular angles α and a parameter n. The same order of accuracy is obtained in the simulation of the elliptic integrals as they are approximated by the fractional powers.