Summary: Special Power Series Solutions
of Linear Differential Equations
Sergei A. Abramov
Computer Center of
the Russian Academy of Science,
Vavilova 40, Moscow 117967, Russia.
Department of Mathematics,
University of Ljubljana,
Jadranska 19, 61111 Ljubljana, Slovenia.
We characterize generalized hypergeometric series that solve a linear differen-
tial equation with polynomial coefficients at an ordinary point of the equation,
and show that these solutions remain hypergeometric at any other ordinary
point. Therefore to find all generalized hypergeometric series solutions, it suf-
fices to look at a finite number of points: all the singular points, and a single,
arbitrarily chosen ordinary point.