Borel-Leroy summability of a nonpolynomial potential

We investigate the perturbation series for the spectrum of a class of Schrödinger operators with potential V = ½x2 + gm−1x2m / (1 + αgx2) which generalize particular cases investigated in the literature in connection with models in laser theory and quantum field theory of particles and fields. It is proved that the series obey a modified strong asymptotic condition of order (m − 1) and have an order (m − 1) strong asymptotic series in g which are shown to be summable in the sense of Borel-Leroy method.