The algebraic closure of the power series field in positive characteristic

For K an algebraically closed field, let K((t)) denote the quotient field o f the power series ring over K. The "Newton-Puiseux theorem" states that if K has characteristic 0, the algebraic closure of K((t)) is the union of th e fields K((t(1/n))) over n is an element of N. We answer a question of Abh yankar by constructing an algebraic closure of K((t)) for any field K of po sitive characteristic explicitly in terms of certain generalized power seri es.