Evaluation of fresnel integrals based on the continued fractions method Original Research Article

We present a simple algorithm for evaluating Fresnel integrals based on the continued fractions method: we use the relation between these integrals and first-kind Bessel functions of fractional order, and we apply a fast code to calculate them based on the continued fractions method. This latter code is especially useful for evaluating high order Bessel functions because it does not require recalculations using normalization relations. Comments on the same procedure but using Millerʹs algorithm to evaluate the required Bessel functions are presented and a comparison with a standard code for evaluating Fresnel integrals (Numerical Recipes program FRENEL) is provided.