 
Summary: D'Alembertian Solutions of Inhomogeneous Linear Equations
(differential, difference, and some other)
Sergei A. Abramov
Computer Center of
the Russian Academy of Science,
Vavilova 40, Moscow 117967, Russia.
abramov@ccas.ru
Eugene V. Zima
Dept. of Computat. Math. & Cybernetics,
Moscow State University,
Moscow 119899, Russia.
zima@cs.msu.su
Abstract
Let an Ore polynomial ring k[X; , ] and a nonzero pseudolinear map : K K, where K is a
, compatible extension of the field k, be given. Then we have the ring k[] of operators K K. It
is assumed that if a firstorder equation Fy = 0, F k[], has a nonzero solution in a , compatible
extension of the field k, then the equation has a nonzero solution in K. These solutions form the set
Hk K of hyperexponential elements. An equation Py = 0, P k[], is called completely factorable if P
can be decomposed in the product of firstorder operators over k. Solutions of all completely factorable
equations form the linear space Ak K of d'Alembertian elements. The order of minimal operator over
