On the algebraic dependence of holonomic functions

Julien Roques; Michael F. Singer

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arXiv · 2011.01717

On the algebraic dependence of holonomic functions

Julien Roques·Michael F. Singer

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Abstract

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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Julien Roques, Michael F. Singer. 2020-11-03. On the algebraic dependence of holonomic functions. https://arxiv.org/abs/2011.01717

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