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In our previous paper I (del Valle--Turbiner, Int. J. Mod. Phys. A34,1950143, 2019) it was developed the formalism to study the general$D$-dimensional radial anharmonic oscillator with potential $V(r)=\frac{1}{g^2}\,\hat{V}(gr)$. It was based on the Perturbation Theory (PT) inpowers of $g$ (weak coupling regime) and in inverse, fractional powers of $g$(strong coupling regime) in both $r$-space and in $(gr)$-space, respectively.As the result it was introduced - the Approximant - a locally-accurate uniformcompact approximation of a wave function. If taken as a trial function invariational calculations it has led to variational energies of unprecedentedaccuracy for cubic anharmonic oscillator. In this paper the formalism isapplied to both quartic and sextic, spherically-symmetric radial anharmonicoscillators with two term potentials $V(r)= r^2 + g^{2(m-1)}\, r^{2m}, m=2,3$,respectively. It is shown that a two-parametric Approximant for quarticoscillator and a five-parametric one for sextic oscillator for the first foureigenstates used to calculate the variational energy are accurate in 8-12figures for any $D=1,2,3\ldots $ and $g \geq 0$, while the relative deviationof the Approximant from the exact eigenfunction is less than $10^{-6}$ for any$r \geq 0$.

international journal of modern physics a

Radial Anharmonic Oscillator: Perturbation Theory, New Semiclassical  Expansion, Approximating Eigenfunctions. II. Quartic and Sextic Anharmonicity  Cases