We study the form of possible algebraic relations between functions satisfying linear differential equations. In particular, if and satisfy linear differential equations and are algebraically dependent, we give conditions on the differential Galois group associated to guaranteeing that is a polynomial in . We apply this to hypergeometric functions and iterated integrals.
[Mag94] Lectures on differential Galois theory, University Lecture Series, 7, American Mathematical Society, 1994 | Zbl: 0855.12001
[Mit96] Differential Galois groups of confluent generalized hypergeometric equations: an approach using Stokes multipliers, Pac. J. Math., Volume 176 (1996) no. 2, pp. 365-405 | Article | MR: MR1434997 | Zbl: 0883.12004