Numerical methods for the computation of the confluent and Gauss hypergeometric functions
Numerical methods for the computation of the confluent and Gauss hypergeometric functions
复制标题
计算合流函数和高斯超几何函数的数值方法
DOI：
10.1007/s11075-016-0173-0
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发表时间：
2014
影响因子：
2.1
通讯作者：
M. Porter
中科院分区：
文献类型：
--
作者：
J. Pearson;S. Olver;M. Porter
两个最常用的超几何函数是合流超几何函数和高斯超几何函数。我们回顾了现有的技术，准确，快速，可靠的计算这两个超几何函数在不同的参数和变量制度。我们调查的方法包括泰勒和渐近级数计算，高斯-雅可比求积，微分方程的数值解，递归关系，和其他。我们讨论的数值实验的结果，用于确定最佳的方法，在实践中，每个参数和变量政权考虑。我们提供了“路线图”，并建议在每种情况下应使用哪些方法。
The two most commonly used hypergeometric functions are the confluent hypergeometric function and the Gauss hypergeometric function. We review the available techniques for accurate, fast, and reliable computation of these two hypergeometric functions in different parameter and variable regimes. The methods that we investigate include Taylor and asymptotic series computations, Gauss–Jacobi quadrature, numerical solution of differential equations, recurrence relations, and others. We discuss the results of numerical experiments used to determine the best methods, in practice, for each parameter and variable regime considered. We provide “roadmaps” with our recommendation for which methods should be used in each situation.