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<p>The Gauss hypergeometric function unifies many special functions encountered in physics, engineering, as well as many other applied sciences. With its prominence across disciplines, numerous methods have been developed to compute it for any value of its argument and its three additional parameters. However, these methods of computation are either slower than desired or don’t offer the accuracy needed in many applications. Taking advantage of a conformal mapping in conjunction with the numerous connection or transformation formulas, we have developed a fast and accurate method for evaluation in double precision arithmetic.</p>

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Efficient and accurate evaluation of the Gauss hypergeometric function

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年7月10日

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  • Caleb Jacobs,
  • Cécile Piret,
  • Bengt Fornberg

摘要

The Gauss hypergeometric function unifies many special functions encountered in physics, engineering, as well as many other applied sciences. With its prominence across disciplines, numerous methods have been developed to compute it for any value of its argument and its three additional parameters. However, these methods of computation are either slower than desired or don’t offer the accuracy needed in many applications. Taking advantage of a conformal mapping in conjunction with the numerous connection or transformation formulas, we have developed a fast and accurate method for evaluation in double precision arithmetic.