Phenomenological applications of rational approximants

We illustrate the powerfulness of Padé approximants (PAs) as a summation method and explore one of their extensions, the so-called quadratic approximant (QAs), to access both space- and (low-energy) time-like (TL) regions. As an introductory and pedagogical exercise, the function
1
𝑧

⁢ln⁡(1+𝑧)
is approximated by both kind of approximants. Then, PAs are applied to predict pseudoscalar meson Dalitz decays and to extract 𝑉𝑢⁢𝑏
from the semileptonic 𝐵→𝜋⁢ℓ⁢𝜈ℓ
decays. Finally, the 𝜋
vector form factor in the TL region is explored using QAs.