On functions K and E generated by a sequence of moments

2016/08/25 by Avner Kiro, Mikhail Sodin, Kiro, Avner +1
Mathematics · #Classical Analysis and ODEs (math.CA) #Complex Variables (math.CV) #FOS: Mathematics #Meromorphic and Entire Functions

paper · pdf · doi:10.48550/arxiv.1608.07147

openalex publication_date 2016/08/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the asymptotic behaviour of the entire function E(z) = ∑_{n≥ 0} (zⁿ)/(γ(n+1)) and the analytic function K(z) = \frac12π\rm i ∫_c-\rm i∞^c+\rm i∞ z^-sγ(s) \rm ds , which naturally appear in various classical problems of analysis.

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