  We develop a method for computing series expansions for solutions to ordinary
differential equations when the asymptotic form contains both linear and
logarithmic terms. Such situations are common in primordial cosmology when
considering series expansions out of a singularity in the equations arising
from a pre-inflationary phase of the universe. We develop mathematical
techniques for generating these series expansions, and apply them to polynomial
and Starobinsky inflationary potentials with kinetic initial conditions. Code
for analytic and numerical computation of logolinear series is provided on
GitHub.
