  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) in
powers 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 uniform
compact approximation of a wave function. If taken as a trial function in
variational calculations it has led to variational energies of unprecedented
accuracy for cubic anharmonic oscillator. In this paper the formalism is
applied to both quartic and sextic, spherically-symmetric radial anharmonic
oscillators 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 quartic
oscillator and a five-parametric one for sextic oscillator for the first four
eigenstates used to calculate the variational energy are accurate in 8-12
figures for any $D=1,2,3\ldots $ and $g \geq 0$, while the relative deviation
of the Approximant from the exact eigenfunction is less than $10^{-6}$ for any
$r \geq 0$.
