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Real values of the $W$-function. (English) Zbl 0886.65010
Summary: Approximations for real values of $W(x)$, where $W$ is defined by solutions of $W \exp(W) = x$, are presented. All of the approximations have maximum absolute $(|W|>1)$ or relative $(|W|<1)$ errors of $O(10^{-4})$. With these approximations an efficient algorithm, consisting of a single iteration of a rapidly converging iteration scheme, gives estimates of $W(x)$ accurate to at least 16 significant digits (15 digits if double precision is used). The Fortran code resulting from the algorithm is written to account for the different floating-point-number mantissa lengths on different computers, so that $W(x)$ is computed to the floating-point precision available on the host machine.

65D20Computation of special functions, construction of tables
33B10Exponential and trigonometric functions
Maple; WAPR
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