Abstract
Abstract
We develop multisummability, in the positive real direction, for generalized power series with natural support, and we prove o-minimality of the expansion of the real field by all multisums of these series. This resulting structure expands both
$\mathbb {R}_{\mathcal {G}}$
and the reduct of
$\mathbb {R}_{\text {an}^*}$
generated by all convergent generalized power series with natural support; in particular, its expansion by the exponential function defines both the gamma function on
$(0,\infty )$
and the zeta function on
$(1,\infty )$
.
Publisher
Canadian Mathematical Society