We show the existence of an o-minimal expansion of the real field which defines both the Gamma function on $(0,\infty)$ and the Zeta function on $(1\infty)$.
To this end, we develop multisummability for generalized power series with natural support, and we prove o-minimality of the expansion of the real field by all multisums of those series that are multisummable in the positive real direction.

This is joint work with Tamara Servi and Patrick Speissegger.