Case study of the convergency of nonlinear perturbation series: Morse-Feshbach nonlinear series

We study the divergent behavior of the Morse-Feshbach nonlinear perturbatio n series (MFNS) [P. M. Morse and H. Feshbach, Methods of Theoretical Physic s, Part II (McGraw-Hill, New York, 1953)] for producing convergent energy l evels using the ground state of a quartic anharmonic oscillator (AHO) in th e strong coupling limit. Numerical calculations have been done up to tenth order. Further comparison of the MFNS convergent result has been made with the matrix diagonalization method.