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<a name="Relative-Exponential-Functions"></a>
<div class="header">
<p>
Next: <a href="Exponentiation-With-Error-Estimate.html#Exponentiation-With-Error-Estimate" accesskey="n" rel="next">Exponentiation With Error Estimate</a>, Previous: <a href="Exponential-Function.html#Exponential-Function" accesskey="p" rel="previous">Exponential Function</a>, Up: <a href="Exponential-Functions.html#Exponential-Functions" accesskey="u" rel="up">Exponential Functions</a> &nbsp; [<a href="Function-Index.html#Function-Index" title="Index" rel="index">Index</a>]</p>
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<hr>
<a name="Relative-Exponential-Functions-1"></a>
<h4 class="subsection">7.16.2 Relative Exponential Functions</h4>

<dl>
<dt><a name="index-gsl_005fsf_005fexpm1"></a>Function: <em>double</em> <strong>gsl_sf_expm1</strong> <em>(double <var>x</var>)</em></dt>
<dt><a name="index-gsl_005fsf_005fexpm1_005fe"></a>Function: <em>int</em> <strong>gsl_sf_expm1_e</strong> <em>(double <var>x</var>, gsl_sf_result * <var>result</var>)</em></dt>
<dd><p>These routines compute the quantity <em>\exp(x)-1</em> using an algorithm
that is accurate for small <em>x</em>.
</p></dd></dl>

<dl>
<dt><a name="index-gsl_005fsf_005fexprel"></a>Function: <em>double</em> <strong>gsl_sf_exprel</strong> <em>(double <var>x</var>)</em></dt>
<dt><a name="index-gsl_005fsf_005fexprel_005fe"></a>Function: <em>int</em> <strong>gsl_sf_exprel_e</strong> <em>(double <var>x</var>, gsl_sf_result * <var>result</var>)</em></dt>
<dd><p>These routines compute the quantity <em>(\exp(x)-1)/x</em> using an
algorithm that is accurate for small <em>x</em>.  For small <em>x</em> the
algorithm is based on the expansion <em>(\exp(x)-1)/x = 1 + x/2 +
x^2/(2*3) + x^3/(2*3*4) + \dots</em>.
</p></dd></dl>

<dl>
<dt><a name="index-gsl_005fsf_005fexprel_005f2"></a>Function: <em>double</em> <strong>gsl_sf_exprel_2</strong> <em>(double <var>x</var>)</em></dt>
<dt><a name="index-gsl_005fsf_005fexprel_005f2_005fe"></a>Function: <em>int</em> <strong>gsl_sf_exprel_2_e</strong> <em>(double <var>x</var>, gsl_sf_result * <var>result</var>)</em></dt>
<dd><p>These routines compute the quantity <em>2(\exp(x)-1-x)/x^2</em> using an
algorithm that is accurate for small <em>x</em>.  For small <em>x</em> the
algorithm is based on the expansion <em>2(\exp(x)-1-x)/x^2 = 
1 + x/3 + x^2/(3*4) + x^3/(3*4*5) + \dots</em>.
</p></dd></dl>

<dl>
<dt><a name="index-gsl_005fsf_005fexprel_005fn"></a>Function: <em>double</em> <strong>gsl_sf_exprel_n</strong> <em>(int <var>n</var>, double <var>x</var>)</em></dt>
<dt><a name="index-gsl_005fsf_005fexprel_005fn_005fe"></a>Function: <em>int</em> <strong>gsl_sf_exprel_n_e</strong> <em>(int <var>n</var>, double <var>x</var>, gsl_sf_result * <var>result</var>)</em></dt>
<dd><p>These routines compute the <em>N</em>-relative exponential, which is the
<var>n</var>-th generalization of the functions <code>gsl_sf_exprel</code> and
<code>gsl_sf_exprel_2</code>.  The <em>N</em>-relative exponential is given by,
</p>
<div class="example">
<pre class="example">exprel_N(x) = N!/x^N (\exp(x) - \sum_{k=0}^{N-1} x^k/k!)
            = 1 + x/(N+1) + x^2/((N+1)(N+2)) + ...
            = 1F1 (1,1+N,x)
</pre></div>
</dd></dl>






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