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Fractional power approximations of elliptic integrals and bessel functions

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  • Kobayashi, Yasuhiro
  • Ohkita, Masaaki
  • Inoue, Michio

Abstract

In the previous papers [1]∽[3], fractional powers were used to approximate elementary functions and their usefulness was proved with experimental results. In the present paper, some further investigations are reported. That is, elliptic integrals in Legendre's canonical form and Bessel functions are approximated by fractional powers. As the fractional power approximation, f(x) ⋍ c0 + c1x + c2xp is discussed. When all coefficients c0, c1, c2, p are properly assigned, the accuracy of this approximation becomes comparable to that of the Chebyshev approximation using polynomials up to the third degree.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:matcom:v:20:y:1978:i:4:p:285-290
    DOI: 10.1016/0378-4754(78)90020-4
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    1. 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. 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.
    2. Tanaka, Toshijiro & Fujisaka, Hirokazu & Inoue, Masayoshi, 1994. "Fluctuations of the specific heat in one-dimensional dilute Ising models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 206(1), pages 13-24.

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    1. 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.
    2. Kobayashi, Yasuhiro & Ohkita, Masaaki & Inoue, Michio, 1977. "Generation of two-variable functions based on the polynomial approximation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 19(2), pages 141-149.

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