Lambert's problem, to find the unique conic trajectory that connects two
points in a spherical gravity field in a given time, is represented by a set of
transcendental equations due to Lagrange. The associated Lagrange equations for the orbital transfer time may be expressed as series expansions
for all cases. Power series solutions have been published that reverse the
functionality of the Lagrange equations to provide direct expressions for the
unknown semi-major axis as an explicit function of time. The convergence
behavior of the series solutions is examined over the range of possible transfer angles and flight times. The effect of arbitrary precision calculations is
shown on the generation of the series coefficients.