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This article studies the problem of approximating functions belonging to aHilbert space $\mathcal H_d$ with a reproducing kernel of the form $$\tildeK_d(\boldsymbol x,\boldsymbol t):=\prod_{\ell=1}^d\left(1-\alpha_\ell^2+\alpha_\ell^2K_{\gamma_\ell}(x_\ell,t_\ell)\right)\ \ \\mbox{for all} \ \ \ \boldsymbol x,\boldsymbol t\in\mathbb R^d.$$ The$\alpha_\ell\in[0,1]$ are scale parameters, and the $\gamma_\ell>0$ aresometimes called shape parameters. The reproducing kernel $K_{\gamma}$corresponds to some Hilbert space of functions defined on $\mathbb R$. Thekernel $\tilde K_d$ generalizes the anisotropic Gaussian reproducing kernel,whose tractability properties have been established in the literature. Wepresent sufficient conditions on $\{\alpha_\ell\gamma_\ell\}_{\ell=1}^{\infty}$ under which polynomial tractability holds forfunction approximation problems on $\mathcal H_d$. The exponent of strongpolynomial tractability arises from bounds on the eigenvalues of a positivedefinite linear operator.

Tractability of the function approximation problem in terms of the kernel's shape and scale parameters