The Lambert W-functions and some of their integrals: a case study of high-precision computation

@article{Gautschi2010TheLW,
  title={The Lambert W-functions and some of their integrals: a case study of high-precision computation},
  author={Walter Gautschi},
  journal={Numerical Algorithms},
  year={2010},
  volume={57},
  pages={27-34}
}
The real-valued Lambert W-functions considered here are w 0(y) and w  − 1(y), solutions of we w  = y, − 1/e < y < 0, with values respectively in ( − 1,0) and ( − ∞ , − 1). A study is made of the numerical evaluation to high precision of these functions and of the integrals $\int_1^\infty [-w_0(-xe^{-x})]^\alpha x^{-\beta}\d x$ , α > 0, β ∈ ℝ, and $\int_0^1 [-w_{-1}(-x e^{-x})]^\alpha x^{-\beta}\d x$ , α > − 1, β < 1. For the latter we use known integral representations and their evaluation by… CONTINUE READING

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