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

Author

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  • Kobayashi, Y.
  • Ohkita, M.
  • Inoue, M.

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.

Suggested Citation

  • Kobayashi, Y. & Ohkita, M. & Inoue, M., 1979. "On the use of an exponential function in approximation of elliptic integrals," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 21(2), pages 226-230.
    • Handle: RePEc:eee:matcom:v:21:y:1979:i:2:p:226-230
    DOI: 10.1016/0378-4754(79)90138-1
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    1. Kobayashi, Yasuhiro & Ohkita, Masaaki & Inoue, Michio, 1978. "Fractional power approximations of elliptic integrals and bessel functions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 20(4), pages 285-290.
    2. Kobayashi, Yasuhiro & Ohkita, Masaaki & Inoue, Michio, 1976. "Fractional power approximation and its generation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 18(2), pages 115-122.
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    Cited by:

    1. van der Linden, J. & Capel, H.W. & Nijhoff, F.W., 1989. "Linear integral equations and multicomponent nonlinear integrable systems II," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 160(2), pages 235-273.

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