High accuracy approximation for the modified Bessel function of fractional order I1/3(x)

Abstract

The modified Bessel functions of fractional order I1/3(x) has been approximated by an analytic function containing rational and hyperbolic fumctions. A technique using both power series and assymptotic expansion has been used. The accuracy of the approximation is very high using only three parameters., and the largest relative error is smaller than 0,004.