Computing hypergeometric functions rigorously
Language
en
Article de revue
This item was published in
ACM Transactions on Mathematical Software. 2019-08-08, vol. 45, n° 3, p. 1-26
Association for Computing Machinery
English Abstract
We present an efficient implementation of hypergeometric functions in arbitrary-precision interval arithmetic. The functions 0F1, 1F1, 2F1 and 2F0 (or the Kummer U-function) are supported for unrestricted complex parameters ...Read more >
We present an efficient implementation of hypergeometric functions in arbitrary-precision interval arithmetic. The functions 0F1, 1F1, 2F1 and 2F0 (or the Kummer U-function) are supported for unrestricted complex parameters and argument, and by extension, we cover exponential and trigonometric integrals, error functions, Fresnel integrals, incomplete gamma and beta functions, Bessel functions, Airy functions, Legendre functions, Jacobi polynomials, complete elliptic integrals, and other special functions. The output can be used directly for interval computations or to generate provably correct floating-point approximations in any format. Performance is competitive with earlier arbitrary-precision software, and sometimes orders of magnitude faster. We also partially cover the generalized hypergeometric function pFq and computation of high-order parameter derivatives.Read less <
English Keywords
orthogonal polynomials
Bessel functions
arbitrary-precision arithmetic
hypergeometric functions
interval arithmetic
automatic differentiation
European Project
Algorithmic Number Theory in Computer Science
Origin
Hal imported