Highly Influenced

15 Excerpts

@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} }

- Published in Numerical Algorithms 2010
DOI:10.1007/s11075-010-9409-6

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