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We present our recent results on the hadronic light-by-lightpseudoscalar-exchange contribution to the anomalous magnetic moment of the muonusing rational approximants. Our work provides a generalization of Pad\'eapproximants to the bivariate case to describe the most general doubly-virtualtransition form factor, which is required in the calculation. This methodprovides a powerful tool to systematically implement the known experimentaldata on transition form factors in the space-like region and low energies in amodel-independent way. Given the lack of experimental data on thedoubly-virtual transition form factor, we make use of the pseduoscalar decaysinto lepton pairs. We find an interesting and puzzling situation which callsfor new experimental measurements to clarify the present state.

Pseudoscalar-exchange contribution to $(g-2)_{\mu}$ from rational approximants