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We present a new algorithm for computing hyperexponential solutions ofordinary linear differential equations with polynomial coefficients. Thealgorithm relies on interpreting formal series solutions at the singular pointsas analytic functions and evaluating them numerically at some common ordinarypoint. The numerical data is used to determine a small number of combinationsof the formal series that may give rise to hyperexponential solutions.

Finding Hyperexponential Solutions of Linear ODEs by Numerical Evaluation