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arxiv: 1011.5940 · v1 · pith:Z6MYZPIMnew · submitted 2010-11-27 · 🧮 math.CA

Unimodal sequences show Lambert W is Bernstein

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keywords functionlambertbernsteinpositivesequenceunimodalappearingbranch
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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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