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Faculty of Mathematics and Physics, Charles University, Ke Karlovu 3, 12116 Prague 2, Czech Republic: Large-order behaviour of the strong coupling perturbation expansion for anharmonic oscillators

A new formula describing the large-order behaviour of the strong coupling perturbation coefficients for the anharmonic oscillators with the Hamiltonian is suggested. A new method for the accurate calculation of the square root branch points of the energy from the numerical values of the coefficients is also suggested. The branch points and the related minimal values of the coupling constant for which the expansion converges are calculated for the ground state of the quartic, sextic, octic and decadic oscillators.