关于完整函数的代数相关性

J. Roques, M. Singer
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引用次数: 0

摘要

我们研究满足线性微分方程的函数之间可能的代数关系的形式。特别地,如果f和g满足线性微分方程并且是代数相关的,我们给出了与f相关的微分伽罗瓦群保证g是f中的多项式的条件。我们将其应用于超几何函数和迭代积分。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
On the algebraic dependence of holonomic functions
We study the form of possible algebraic relations between functions satisfying linear differential equations. In particular , if f and g satisfy linear differential equations and are algebraically dependent, we give conditions on the differential Galois group associated to f guaranteeing that g is a polynomial in f. We apply this to hypergeometric functions and iterated integrals.
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