An Analytic Approximation for the Modified Bessel Function of Negative Fractional Order I−2\(_{/3}\)(x)
Pablo Martin *
Department of Physics, Universidad de Antofagasta, Antofagasta, Chile.
Jorge Olivares
Department of Mathematics, Universidad de Antofagasta, Antofagasta, Chile.
Fernando Maass
Department of Physics, Universidad de Antofagasta, Antofagasta, Chile.
*Author to whom correspondence should be addressed.
Abstract
The modified Bessel functions appear in Electrodynamics and other areas of Physics. In the present work, an analytic approximation to the modified Bessel function of negative fractional order I-2/3 (x) is presented. The validity of the approximation is for every positive value of the independent variable. The accuracy is high in spite of the small number (4) of parameters used. The approximation is a combination of elementary functions with rational ones. Power series and asymptotic expansions are simultaneously used to obtain the approximation.
Keywords: Bessel functions, maximum relative error, power series, asymptotic expansions