Risch算法是用于不定积分的判定程序，它确定给定的积分是否是初等函数，如果是，则返回积分的闭合形式结果。它构建了对数、指数和代数扩展的塔。代数扩展的情况非常复杂，因此尚未在任何计算机代数系统中完全实现。刘维尔原理可以追溯到 19 世纪，是 Risch 算法的重要组成部分。Risch 算法有一些扩展，特别是 Cherry 的扩展，可以处理一些特殊函数。
Risch算法
另请参阅
初等函数, Horowitz 约化, 不定积分, 刘维尔原理此条目由 Bhuvanesh Bhatt 贡献
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参考文献
Bronstein, M. Symbolic Integration I: Transcendental Functions. New York: Springer-Verlag, 1997.Cherry, G. W. Algorithms for Integrating Elementary Functions in Terms of Logarithmic Integrals and Error Functions. Ph.D. thesis. University of Delaware, 1983.Cherry, G. W. "Integration in Finite Terms with Special Functions: The Logarithmic Integral." SIAM J. Computing 15, 1-12, 1986.Cherry, G. W. "An Analysis of the Rational Exponential Integral." SIAM J. Computing 18, 893-905, 1989.Davenport, J. H. On the Integration of Algebraic Functions. Berlin: Springer-Verlag, 1981.Geddes, K. O.; Czapor, S. R.; and Labahn, G. "The Risch Integration Algorithm." Ch. 12 in Algorithms for Computer Algebra. Amsterdam, Netherlands: Kluwer, pp. 511-573, 1992.Risch, R. "On the Integration of Elementary Functions Which are Built Up using Algebraic Operations." Report SP-2801/002/00. Santa Monica, CA: Sys. Dev. Corp., 1968.Risch, R. "The Problem of Integration in Finite Terms." Trans. Amer. Math. Soc. 139, 167-189, 1969.Risch, R. "The Solution of the Problem of Integration in Finite Terms." Bull. Amer. Math. Soc., 1-76, 605-608, 1970.Risch, R. "Algebraic Properties of Elementary Functions of Analysis." Amer. J. Math. 101, 743-759, 1979.在 Wolfram|Alpha 中被引用
Risch算法引用为
Bhatt, Bhuvanesh. "Risch算法." 来自 MathWorld--Wolfram Web 资源, 由 Eric W. Weisstein 创建. https://mathworld.net.cn/RischAlgorithm.html