  We present our recent results on the hadronic light-by-light
pseudoscalar-exchange contribution to the anomalous magnetic moment of the muon
using rational approximants. Our work provides a generalization of Pad\'e
approximants to the bivariate case to describe the most general doubly-virtual
transition form factor, which is required in the calculation. This method
provides a powerful tool to systematically implement the known experimental
data on transition form factors in the space-like region and low energies in a
model-independent way. Given the lack of experimental data on the
doubly-virtual transition form factor, we make use of the pseduoscalar decays
into lepton pairs. We find an interesting and puzzling situation which calls
for new experimental measurements to clarify the present state.
