Sound field reproduction using high-order Ambisonics (HOA) is limited to a small listening region. This is a consequence of HOA relying on a loudspeaker array to re-create, term-by-term, the lower orders of the sound field's multipole expansion. However, results from perturbation theory show that partial sums of asymptotic series can be transformed into other sequences with faster convergence; this is known as series acceleration. This study considers the use of series acceleration to improve the accuracy of sound field reproduction away from the origin. This may lead to a larger listening region compared to conventional HOA. The behavior of the proposal is evaluated numerically and its potential use in sound field reproduction is discussed.