Large-order behaviour of the strong coupling perturbation expansion for anharmonic oscillators

A new formula describing the large-order behaviour of the strong coupling p erturbation coefficients for the anharmonic oscillators with the Hamiltonia n H = -d(2)/dx(2) + x(2) + beta x(2m) is suggested. A new method for the ac curate calculation of the square root branch points of the energy from the numerical values of the coefficients is also suggested. The branch points a nd the related minimal values of the coupling constant beta for which the e xpansion converges are calculated for the ground state of the quartic, sext ic, octic and decadic oscillators.