Guessing singular dependencies


Given complex numbers , it is classical that linear dependencies with can be guessed using the LLL-algorithm. Similarly, given formal power series , algorithms for computing Padé-Hermite forms provide a way to guess relations with . Assuming that have a radius of convergence and given a real number , we will describe a new algorithm for guessing linear dependencies of the form , where have a radius of convergence . We will also present two alternative algorithms for the special cases of algebraic and Fuchsian dependencies.

Keywords: guessing, asymptotic dependency, analytic continuation, orthogonalization, Fuchsian singularity, Padé-Hermite forms, algorithm

A.M.S. subject classification: 30E10, 30B40, 41A21, 65B05

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