D'Alembertian Solutions of Linear Differential and Difference Equations

  title={D'Alembertian Solutions of Linear Differential and Difference Equations},
  author={Sergei A. Abramov and Marko Petkovsek},
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 <italic>Ly = 0</italic>, one can write down the corresponding solutions of <italic>Ly = f</italic> and of <italic>L<supscrpt>*</supscrpt>y = 0</italic>. 
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