Unimodal sequences show Lambert W is Bernstein

2010/11/27 by G. A. Kalugin, Kalugin, G. A., David J. Jeffrey +2
Engineering · Mathematics · Physics and Astronomy · #11B83 #Classical Analysis and ODEs (math.CA) #Experimental and Theoretical Physics Studies #FOS: Mathematics #Sports Dynamics and Biomechanics #math.CA #msc:11B83

paper · pdf · doi:10.48550/arxiv.1011.5940

6 pages

arxiv created 2010/11/27 · openalex publication_date 2010/11/27 · arxiv updated 2010/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider a sequence of polynomials appearing in expressions for the derivatives of the Lambert W function. The coefficients of each polynomial are shown to form a positive sequence that is log-concave and unimodal. This property implies that the positive real branch of the Lambert W function is a Bernstein function.

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