We give an overview of published algorithms by our group and of current activities and future plans. In particular we give details on methods for computing special functions and discuss in detail two current lines of research. Firstly, we describe the recent developments for the computation of central and non-central $\chi$-square cumulative distributions (also called Marcum $Q-$functions), and we present a new quadrature method for computing them. Secondly, we describe the fourth order methods for computing zeros of special functions recently developed, and we provide an explicit example for the computation of complex zeros of Bessel functions. We end with an overview of published software by our group for computing special functions.

Additional Metadata
Keywords special functions, incomplete gamma functions, Marcum's Q-function, algorithms, power series, asymptotic expansions, recurrence relations, continued fractions, numerical quadrature
MSC Computation of special functions, construction of tables (msc 65D20)
THEME Software (theme 1)
Persistent URL dx.doi.org/10.1016/j.scico.2013.11.004
Journal Science of Computer Programming
Note Special issue on Numerical Software: Design, Analysis and Verification
Gil, A, Segura, J, & Temme, N.M. (2014). Recent software developments for special functions in the Santander-Amsterdam project. Science of Computer Programming, 90(Part A), 42–54. doi:10.1016/j.scico.2013.11.004