A code to evaluate modified bessel functions based on thecontinued fraction method Original Research Article

We present an algorithm to evaluate the modified Bessel functions Iv and Kv of integral and half-integral order based onthe calculation of the continued fraction for the IvIs, the Wronskian and the application of forward recurrence relations for the KvI s and backward recurrence for the IvI s. The main feature of the algorithm is that it does not require recalculations using normalization relations nor trial values to start the recurrences; the code evaluates in each step (already normalized) Bessel functions. The accuracy of the method (10−16 for half-integral order and better than 2×10−7 for integral order in our code) is limited only by the precision in the initial values for the recurrence and the maximum order available for a given value of the argument is restricted only by the maximum real number available in the computer.