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Pré-Publication, Document De Travail Année : 2020

On the algebraic dependence of holonomic functions

Résumé

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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Dates et versions

hal-02986384 , version 1 (02-11-2020)

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Julien Roques, Michael F. Singer. On the algebraic dependence of holonomic functions. 2020. ⟨hal-02986384⟩
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