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<title>Lambert W Functions - GNU Scientific Library -- Reference Manual</title>
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<h3 class="section">7.23 Lambert W Functions</h3>
<p><a name="index-W-function-672"></a><a name="index-Lambert-function-673"></a>
Lambert's W functions, W(x), are defined to be solutions
of the equation W(x) \exp(W(x)) = x. This function has
multiple branches for x < 0; however, it has only
two real-valued branches. We define W_0(x) to be the
principal branch, where W > -1 for x < 0, and
<!-- {$W_{-1}(x)$} -->
W_{-1}(x) to be the other real branch, where
W < -1 for x < 0. The Lambert functions are
declared in the header file <samp><span class="file">gsl_sf_lambert.h</span></samp>.
<div class="defun">
— Function: double <b>gsl_sf_lambert_W0</b> (<var>double x</var>)<var><a name="index-gsl_005fsf_005flambert_005fW0-674"></a></var><br>
— Function: int <b>gsl_sf_lambert_W0_e</b> (<var>double x, gsl_sf_result * result</var>)<var><a name="index-gsl_005fsf_005flambert_005fW0_005fe-675"></a></var><br>
<blockquote><p>These compute the principal branch of the Lambert W function, W_0(x).
<!-- exceptions: GSL_EDOM, GSL_EMAXITER -->
</p></blockquote></div>
<div class="defun">
— Function: double <b>gsl_sf_lambert_Wm1</b> (<var>double x</var>)<var><a name="index-gsl_005fsf_005flambert_005fWm1-676"></a></var><br>
— Function: int <b>gsl_sf_lambert_Wm1_e</b> (<var>double x, gsl_sf_result * result</var>)<var><a name="index-gsl_005fsf_005flambert_005fWm1_005fe-677"></a></var><br>
<blockquote><p>These compute the secondary real-valued branch of the Lambert W function,
<!-- {$W_{-1}(x)$} -->
W_{-1}(x).
<!-- exceptions: GSL_EDOM, GSL_EMAXITER -->
</p></blockquote></div>
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