Recursive Solutions of Lagrangian Perturbation Theory
  In the standard perturbation theory (SPT) of self-gravitating Newtonian fluid
in an expanding universe, recurrence relations for higher-order solutions are
well known and play an important role both in practical applications and in
theoretical investigations. The recurrence relations in Lagrangian perturbation
theory (LPT), however, had not been known for a long time. Recently, two
different kinds of recurrence relations in LPT have been proposed in limited
cases. In this paper, we generalize those methods, and most generally derive
the recurrence relations, which are capable to include any initial condition in
general models of cosmology. The fastest-growing modes in the general relations
are identified, and simplified recurrence relations with accurate approximation
for the time-dependence are obtained.
