Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



The Lambert transform for small and large values of the transformation parameter

Authors: Chelo Ferreira and José L. López
Journal: Quart. Appl. Math. 64 (2006), 515-527
MSC (2000): Primary 41A60, 65R10; Secondary 33B15
DOI: https://doi.org/10.1090/S0033-569X-06-01014-5
Published electronically: August 9, 2006
MathSciNet review: 2259052
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Abstract: We derive asymptotic expansions of the Lambert transform

$\displaystyle \int_0^\infty xt(e^{xt}-1)^{-1}f(t)dt$

of a locally integrable function $ f(t)$ for small and large $ x$. All the expansions are accompanied by error bounds for the remainder at any order of the approximation.

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Additional Information

Chelo Ferreira
Affiliation: Departamento de Matemática Aplicada, Universidad de Zaragoza, Spain
Email: cferrei@unizar.es

José L. López
Affiliation: Departamento de Matemática e Informática, Universidad Pública de Navarra, Spain
Email: jl.lopez@unavarra.es

DOI: https://doi.org/10.1090/S0033-569X-06-01014-5
Keywords: Lambert transform, asymptotic expansions, error bounds
Received by editor(s): November 28, 2005
Published electronically: August 9, 2006
Article copyright: © Copyright 2006 Brown University

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