Fractional power approximations of elliptic integrals and bessel functions

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 + c₂x^p

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.