Special Functions

This project will create a web-based portal enabling users to evaluate a large class of special functions to essentially arbitrary accuracy at user-defined values of input variables.  The special function values will be returned with certificates of accuracy up to hundreds of digits.

Special function evaluation is among the more venerable problems of numerical mathematics and remains a staple for engineers, physicists, and scientific computation.  What is more, the need for detailed numerical evaluations grows steadily as new quantitative theories are developed for an increasing variety of disciplines including biology, finance, and economics.  

This project will provide users with the ability to evaluate a large set of hypergeometric-based special functions to essentially arbitrary accuracy at user-defined input values.  The numerical kernel of the evaluation will be transparent to the user and will rely on the representation of the special function as a continued fraction.  Detailed analysis developed by the Numerical Algorithms Group at the University of Antwerp provides rigorous error bounds based on truncation level of the continued fraction.  The result is a certified level of error on the function values.

This tool will support users who wish to verify independent numerical evaluations of special functions and is aligned with NIST mission to provide standard reference data.