摘要翻译：
一个著名的Klein定理暗示任何具有代数解的超几何微分方程都是少数具有代数解的标准超几何方程之一的后退。最有趣的情况是具有四面体、八面体或二十面体单群的超几何方程。基于代数超几何函数的某些显式（Darboux求值），我们给出了在这些情况下计算Klein回拉覆盖的一个算法。显式表达式可以使用连续关系和最简单的Darboux求值数据库（覆盖Schwarz表）来计算。Klein的回拉变换还在超几何解和具有相同有限单群的标准超几何函数之间导出了代数变换。
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英文标题：
《Transformations of algebraic Gauss hypergeometric functions》
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作者：
Raimundas Vidunas
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最新提交年份：
2008
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分类信息：

一级分类：Mathematics        数学
二级分类：Classical Analysis and ODEs        经典分析与颂歌
分类描述：Special functions, orthogonal polynomials, harmonic analysis, ODE's, differential relations, calculus of variations, approximations, expansions, asymptotics
特殊函数、正交多项式、调和分析、Ode、微分关系、变分法、逼近、展开、渐近
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一级分类：Mathematics        数学
二级分类：Algebraic Geometry        代数几何
分类描述：Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇，叠，束，格式，模空间，复几何，量子上同调
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英文摘要：
  A celebrated theorem of Klein implies that any hypergeometric differential equation with algebraic solutions is a pull-back of one of the few standard hypergeometric equations with algebraic solutions. The most interesting cases are hypergeometric equations with tetrahedral, octahedral or icosahedral monodromy groups. We give an algorithm for computing Klein's pull-back coverings in these cases, based on certain explicit expressions (Darboux evaluations) of algebraic hypergeometric functions. The explicit expressions can be computed using contiguous relations and a data base of simplest Darboux evaluations (covering the Schwarz table). Klein's pull-back transformations also induce algebraic transformations between hypergeometric solutions and a standard hypergeometric function with the same finite monodromy group.
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PDF链接：
https://arxiv.org/pdf/0807.4808