D'Alembertian solutions of linear differential and difference equations

  • Authors:

  • Sergei A. Abramov;Marko Petkovšek

  • Affiliations:

  • Computer Center of the Russian Academy of Science, Vavilova 40, Moscow 117967, Russia;Department of Mathematics and Mechanics, University of Ljubljana, Jadranska 19, 61111 Ljubljana, Slovenia

  • Venue:
  • ISSAC '94 Proceedings of the international symposium on Symbolic and algebraic computation
  • Year:
  • 1994

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Abstract

D'Alembertian solutions of differential (resp. difference) equations are those expressible as nested indefinite integrals (resp. sums) of hyperexponential functions. They are a subclass of Liouvillian solutions, and can be constructed by recursively finding hyperexponential solutions and reducing the order. Knowing d'Alembertian solutions of Ly = 0, one can write down the corresponding solutions of Ly = f and of L*y = 0.