Function evaluation using expansions in Bessel functions of the first kind

An iterative method is proposed for evaluation of fonctions that are expandable in series of Bessel functions of the first kind. The Bessel functions are evaluated by Miller's method, avoiding the need to determine their exact values. As an example, we describe algorithms for evaluation of the integral sine and the normal probability integral with an accuracy of to 10–12 significant digits.Translated from Vychislitel'naya i Prikladnaya Matematika, No. 61, pp. 37–42, 1987.