The pionic contribution to the g-2 of the muon involves a certain integral
over the the modulus squared of F_\pi(t), the pion electromagnetic form factor.
We extend techniques that use cut-plane analyticity properties of F_\pi(t) in
order to account for present day estimates of the pionic contribution and
experimental information at a finite number of points in the space-like region.
Using data from several experiments over a large kinematic range for |t|, we
find bounds on the expansion coefficients of F_\pi(t), sub-leading to the
charge radius. The value of one of these coefficients in chiral perturbation
theory respects these bounds. Furthermore, we present a sensitivity analysis to
the inputs. A brief comparison with results in the literature that use
observables other than the g-2 and timelike data is presented.Comment: 11 pages in EPJ journal style, to appear in European Physical Journal