Finding hyperexponential solutions of linear ODEs by numerical evaluation

  • Authors:

  • Fredrik Johansson;Manuel Kauers;Marc Mezzarobba

  • Affiliations:

  • Johannes Kepler University, Linz, Austria;Johannes Kepler University, Linz, Austria;INRIA, Lyon, France

  • Venue:
  • Proceedings of the 38th international symposium on International symposium on symbolic and algebraic computation
  • Year:
  • 2013

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Abstract

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