Bounds for Substituting Algebraic Functions into D-finite Functions

01/26/2017

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by   Manuel Kauers, et al.

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It is well known that the composition of a D-finite function with an algebraic function is again D-finite. We give the first estimates for the orders and the degrees of annihilating operators for the compositions. We find that the analysis of removable singularities leads to an order-degree curve which is much more accurate than the order-degree curve obtained from the usual linear algebra reasoning.