Abstract

An improved two-point quasifractional approximant method is presented that includes a free parameter in the denominator. This parameter is determined by minimizing the theoretical truncation error bound, thus ensuring high accuracy. An added advantage of introducing a free parameter is that defects that are usual in Pade approximants are always avoided. The method is applied to the fractional Bessel functions J(nu)(x), obtaining a unique approximant, valid for all positive x, that is more accurate than previously published.