Title: Computing the Lambert W function in arbitrary-precision complex interval arithmetic,
Abstract: 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.