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Numerical results for the polaron dispersion are presented for an arbitrarynumber of space dimensions. Upper and lower bounds are calculated for thedispersion curves. They are rather close to each other in the cases of smallelectron-phonon couplings usual for real polar materials. To describe thedispersion in other materials, we suggest a simple fitting formula which can beapplied at intermediate values of the Fr\"ohlich electron-phonon couplingconstant. Its validity is approved by the comparison with direct calculationsand previously obtained results. This makes our results not only reliable andhighly accurate but also easy reproducible.

Upper and lower bounds for the large polaron dispersion in $D=1,2,3$ dimensions