In an earlier paper  we were able to show the existence of asymptotic expansions for the solutions of some regularization procedures fo r higher index differential-algebraic equations in integer powers of the regularization parameter. Recent numerical experiments have led to the conjecture that the asymptotic expansion does not contain the first order term for autonomous systems. In the present note it is proved that this assertion is true for index 2 Hessenberg systems, i.e. convergence of second order with respect to the regularization parameter occurs
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