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Computing the Lambert W function in arbitrary-precision complex interval arithmetic

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Abstract

We describe an algorithm to evaluate all the complex branches of the Lambert W function with rigorous error bounds in arbitrary-precision interval arithmetic or ball arithmetic. The classic 1996 paper on the Lambert W function by Corless et al. provides a thorough but partly heuristic numerical analysis of the Lambert W function which needs to be complemented with some explicit inequalities and practical observations about managing precision and branch cuts. An implementation is provided in the Arb library.

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Acknowledgements

The author thanks the two referees, whose input greatly improved the article.

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  1. INRIA–LFANT, CNRS–IMB–UMR 5251, Université de Bordeaux, 33400, Talence, France

    Fredrik Johansson

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  1. Fredrik Johansson
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Correspondence to Fredrik Johansson.

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Johansson, F. Computing the Lambert W function in arbitrary-precision complex interval arithmetic. Numer Algor 83, 221–242 (2020). https://doi.org/10.1007/s11075-019-00678-x

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