Multisummability for generalized power series

2022/03/28 by Jean-Philippe Rolin, Tamara Servi, Rolin, Jean-Philippe +3
Mathematics · #03C64 #26E10 #Advanced Topology and Set Theory #Approximation Theory and Sequence Spaces #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Equations Stability Results #Logic (math.LO) #Primary 40C10 #Secondary 30D60

paper · pdf · doi:10.48550/arxiv.2203.15047

openalex publication_date 2022/03/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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, its expansion by the exponential function defines both the Gamma function on (0,∞) and the Zeta function on (1,∞).

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