Numerical Calculation of Bessel Functions with Complex Argument for Arbitrary Orders

The rigorous theoretical formula to calculate the first and second kinds of arbitrary real order Bessel functions with complex argument is derived by means of the series expansion in this paper.The modified Bessel functions of the first and second kind with complex argument can also be calculated by these formula.The discrepancy of the numerical results obtained in this paper is compared to those given by the mathematica software package.