Summary: D'Alembertian Solutions
of Linear Di#erential and Di#erence Equations
Sergei A. Abramov
Computer Center of
the Russian Academy of Science,
Vavilova 40, Moscow 117967, Russia.
abramov@sms.ccas.msk.su
Marko PetkovŸsek
Department of Mathematics and Mechanics,
University of Ljubljana,
Jadranska 19, 61111 Ljubljana, Slovenia.
marko.petkovsek@uni­lj.si
Abstract
D'Alembertian solutions 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 corre­
sponding solutions of Ly = f and L # y = 0.
1 Introduction
Let k be a field of characteristic zero, X an indeterminate over k, # a nonzero field­

Source: Abramov, Sergei A. - Dorodnicyn Computing Centre of the Russian Academy of Sciences

Collections: Mathematics; Computer Technologies and Information Sciences