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Multisummability for generalized power series
- Part of
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- Journal:
- Canadian Journal of Mathematics / Volume 76 / Issue 2 / April 2024
- Published online by Cambridge University Press:
- 27 February 2023, pp. 458-494
- Print publication:
- April 2024
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- Article
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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 
$(1,\infty )$.
