  Universal Drinfeld twists are inner automorphisms which relate the coproduct
of a quantum enveloping algebra to the coproduct of the undeformed enveloping
algebra. Even though they govern the deformation theory of classical symmetries
and have appeared in numerous applications, no twist for a semi-simple quantum
enveloping algebra has ever been computed. It is argued that universal twists
can be reconstructed from their well known representations. A method to
reconstruct an arbitrary element of the enveloping algebra from its irreducible
representations is developed. For the twist this yields an algebra valued
generating function to all orders in the deformation parameter, expressed by a
combination of basic and ordinary hypergeometric functions. An explicit
expression for the universal twist of su(2) is given up to third order.
