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Preprint Number 2152

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2152. Jean-Philippe Rolin, Tamara Servi, Patrick Speissegger
Amalgamating the real Gamma and Zeta functions
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Submission date: 28 March 2022.

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 ℝ_G and the reduct of ℝ_{an^*} generated by all convergent generalized power series with natural support; in particular, it defines both the Gamma function on (0,∞) and the Zeta function on (1,∞).

Mathematics Subject Classification: Primary 40C10, 03C64, 26E10, Secondary 30D60

Keywords and phrases:

Full text arXiv 2203.15047: pdf, ps.


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