For given multivariate functions specified by algebraic, differential or difference equations, the separability problem is to decide whether they satisfy linear differential or difference equations in one variable. In this paper, we will explain how separability problems arise naturally in creative telescoping and present some criteria for testing the separability for several classes of special functions, including rational functions, hyperexponential functions, hypergeometric terms, and algebraic functions.

中文翻译：

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创意伸缩中的可分离性问题

对于由代数，微分或差分方程式指定的给定多元函数，可分离性问题是确定它们在一个变量中是否满足线性微分或差分方程式。在本文中，我们将说明可伸缩性问题在创意伸缩中自然产生的原因，并提供一些标准来测试几类特殊功能（包括有理函数，超指数函数，超几何项和代数函数）的可分离性。