Title 



Validated computation of certain hypergeometric functions
 
Author 



 
Abstract 



We present an efficient algorithm for the validated highprecision computation of real continued fractions, accurate to the last digit. The algorithm proceeds in two stages. In the first stage, computations are done in double precision. A forward error analysis and some heuristics are used to obtain an a priori error estimate. This estimate is used in the second stage to compute the fraction to the requested accuracy in high precision (adaptively incrementing the precision for reasons of efficiency). A running error analysis and techniques from interval arithmetic are used to validate the result. As an application, we use this algorithm to compute Gauss and confluent hypergeometric functions when one of the numerator parameters is a positive integer.   
Language 



English
 
Source (journal) 



ACM transactions on mathematical software.  New York, N.Y.  
Publication 



New York, N.Y. : 2011
 
ISSN 



00983500
 
Volume/pages 



38:2(2011), p. 11,111,20
 
Article Reference 



11
 
ISI 



000298638200002
 
Medium 



Eonly publicatie
 
Full text (Publisher's DOI) 


  
