Universal recurrence algorithm for computing Nuttall, generalized Marcum and incomplete Toronto functions and moments of a noncentral χ2 random variable

This article proposes a novel recurrence algorithm for computing Nuttall, generalized Marcum, and incomplete Toronto functions as well as truncated and raw moments (of any real order) for a noncentral χ2 random variable. The numerical results highlight that the proposed recurrence method offers an excellent speed-accuracy trade-off for a wide variety of meaningful and relevant applications ranging from the operations management and industrial engineering fields to problems encountered in the financial engineering industry.