On the algebraic dependence of holonomic functions
Annales Henri Lebesgue, Volume 5 (2022), pp. 141-177.

KeywordsLinear Differential Equations, Differential Galois Theory, Algebraic Relations, Iterated Integrals, Hypergeometric Functions

### 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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