Abstract
The objective of this work is to give expressions for solutions of universal differential equation and finally, as application, provides the unique grouplike solution, by dévissage, of Knizhnik-Zamolodchikov equation satisfying asymptotic conditions, i.e. solution of KZn can be obtained using solution of KZ n−1 and the noncommutative generating series of hyperlogarithms. These expressions are obtained using the algebraic combinatorics on noncommutative formal series with holomorphic coefficients and a Picard-Vessiot theory of noncommutative differential equations.
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