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

Metadata

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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