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In this article, we express solutions of the Gauss hypergeometric equation asa series of the multiple polylogarithms by using iterated integral. Thisrepresentation is the most simple case of a semisimple representation ofsolutions of the formal KZ equation. Moreover, combining this representationwith the connection relations of solutions of the Gauss hypergeometricequation, we obtain various relations of the multiple polylogarithms of onevariable and the multiple zeta values.

Representation of solutions of the Gauss hypergeometric equation by the  multiple polylogarithms, functional relations of the multiple polylogarithms  and relations of the multiple zeta values