Precise analytic approximation for the modified Bessel function I₁(x)

Abstract

Precise analytic approximations have been found for the modified Bessel function $I_1(x)$ of order one. The approximant is simple and with good accuracy for every positive value of the variable $x$. The method to obtain the approximant is an improvement of the multipoint quasi-rational approximation technique, MPQA. This is obtained combining rational functions with elementary auxiliary functions as a bridge function between the power series and asymptotic expansion.