Enigmatic Bessis-type cubic oscillators with real spectra are considered.
Their characteristic relaxation of hermiticity to mere PT symmetry is emphasized.
It is shown tractable by innovative numerical perturbation series.
Their convergence is then addressed as a crucial mathematical problem.
Its detailed analysis is offered in the strong-coupling regime.
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J. Phys. A: Math. Gen. 31 (1998) 10105-12.