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

Y. Kobayashi, M. Ohkita and M. Inoue

Mathematics and Computers in Simulation (MATCOM), 1979, vol. 21, issue 2, 226-230

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) ⋍ c0+c1x+c2epx, 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.

Date: 1979
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:21:y:1979:i:2:p:226-230

DOI: 10.1016/0378-4754(79)90138-1

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