Potential of High Accuracy Approximation for the Modified Bessel Function of Fractional Order \(I_1/3(x)\), Using MPQA Method with Hyperbolic Functions - P. Martin; Jorge Olivaresl; E. Valero (Current Research Progress in Physical Science Vol. 2, 2024)
The modified Bessel functions of fractional order \(I_1/3(x)\) has been approximated by an analytic function containing rational and hyperbolic functions. The Bessel functions the order 1/3 are very important, because its connection with the Airy functions. A technique using both power series and assymptotic expansion has been used. An approximation has been found for the modified Bessel function \(I_1/3(x)\). The accuracy of the approximation is very high using only three parameters., and the largest relative error is smaller than 0,004.