Recent software developments for special functions in the Santander-Amsterdam project

DOI: 
10.1016/j.scico.2013.11.004
Publication date: 
15/09/2014
Main author: 
Gil, Amparo
IAA authors: 
Temme, Nico M.
Authors: 
Gil, Amparo; Segura, Javier; Temme, Nico M.
Journal: 
SCIENCE OF COMPUTER PROGRAMMING
Publication type: 
Article
Volume: 
90
Pages: 
42-54
Number: 
Abstract: 
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. (C) 2013 Elsevier B.V. All rights reserved.
Database: 
WOK
Keywords: 
Special functions; Incomplete gamma functions; Marcum's Q-function; Zeros of special functions; Numerical software