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Continued fraction expansions for the Lambert \(W\) function. (English) Zbl 1414.30007

Summary: In the first part of the paper we give a new integral representation for the principal branch of the Lambert \(W\) function. Then we deduce two continued fraction expansions for this branch. At the end of the paper we study the numerical behavior of the approximants of these expansions.

MSC:

30B70 Continued fractions; complex-analytic aspects

Software:

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Full Text: DOI

Online Encyclopedia of Integer Sequences:

Decimal expansion of 1/(1+LambertW(1)).

References:

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