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Using the results on the electromagnetic pion Form Factor (FF) obtained inthe $O(\alpha_s)$ QCD sum rules with non-local condensates \cite{BPS09} wedetermine the effective continuum threshold for the local duality approach.Then we apply it to construct the $O(\alpha_s^2)$ estimation of the pion FF inthe framework of the fractional analytic perturbation theory.

Pion form factor in QCD sum rules, local duality approach, and O(A_2) fractional analytic perturbation theory