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Proof of a series solution for Euler's trinomial equation
Department of Applied Mathematics, University of Western Ontario, London, ON, Canada.ORCID iD: 0000-0001-8978-5649
2016 (English)In: ACM Communications in Computer Algebra, ISSN 1932-2232, E-ISSN 1932-2240, Vol. 50, no 4, p. 136-144Article in journal (Refereed) Published
Abstract [en]

In 1779, Leonhard Euler published a paper about Lambert's transcendental equation in the symmetric form x(alpha) - x(beta) = (alpha -beta) vx(alpha+beta). In the paper, he studied the series solution of this equation and other results based on an assumption which was not proved in the paper. Euler's paper gave the first series expanion for the so-called Lambert W function. In this work, we briefly review Euler's results and give a proof to modern standards of rigor of the series solution of Lambert's transcendental equation.

Place, publisher, year, edition, pages
New York, USA: Association for Computing Machinery (ACM), 2016. Vol. 50, no 4, p. 136-144
National Category
Mathematics
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URN: urn:nbn:se:kth:diva-247941DOI: 10.1145/3055282.3055284ISI: 000397339600002Scopus ID: 2-s2.0-85014319709OAI: oai:DiVA.org:kth-247941DiVA, id: diva2:1299804
Note

QC 20190404

Available from: 2019-03-28 Created: 2019-03-28 Last updated: 2019-06-11Bibliographically approved

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