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# D'Alembertian Solutions of Linear Differential and Difference Equations

@inproceedings{Abramov1994DAlembertianSO, title={D'Alembertian Solutions of Linear Differential and Difference Equations}, author={Sergei A. Abramov and Marko Petkovsek}, booktitle={ISSAC}, year={1994} }

- Published 1994 in ISSAC
DOI:10.1145/190347.190412

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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