SEXTIC AND OCTIC ANHARMONIC-OSCILLATORS - CONNECTION BETWEEN STRONG-COUPLING AND WEAK-COUPLING EXPANSIONS

For the eigenvalues of the Hamiltonians 1/2 (p) over cap(2) + 1/2x(2) + 1/2 beta x(2m) With m = 3, 4..., we propose representations reproduc ing the well known weak-coupling asymptotic perturbation and strong-co upling expansions as limiting cases. Some analytical relations which t he strong-coupling coefficients must satisfy are presented.