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

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arxiv 1705.03266 v1 pith:25YXRLCI submitted 2017-05-09 cs.MS cs.NAmath.NA

Fredrik Johansson This is my paper · ORCID
classification cs.MScs.NAmath.NA
keywords functionlambertarithmeticcomplexintervalalgorithmanalysisarbitrary-precision
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We describe an algorithm to evaluate all the complex branches of the Lambert W function with rigorous error bounds in interval arithmetic, which has been implemented in the Arb library. The classic 1996 paper on the Lambert W function by Corless et al. provides a thorough but partly heuristic numerical analysis which needs to be complemented with some explicit inequalities and practical observations about managing precision and branch cuts.

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Cited by 1 Pith paper

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  1. Self-Referential Leading Digits of Exponential Sequences: Arithmetic Structure and Certified Search

    math.NT 2026-07 accept novelty 7.0 of 10

    Self-prefix hits of c^m admit exact discrepancy identities, Lambert two-gap candidates, resonance rigidity, and certified O(N^{1-1/ν} polylog N) search; infinitude of 2^m starting with m remains open.

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