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<title>GNU Scientific Library &ndash; Reference Manual: Irregular Modified Cylindrical Bessel Functions</title>

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<a name="Irregular-Modified-Cylindrical-Bessel-Functions"></a>
<div class="header">
<p>
Next: <a href="Regular-Spherical-Bessel-Functions.html#Regular-Spherical-Bessel-Functions" accesskey="n" rel="next">Regular Spherical Bessel Functions</a>, Previous: <a href="Regular-Modified-Cylindrical-Bessel-Functions.html#Regular-Modified-Cylindrical-Bessel-Functions" accesskey="p" rel="previous">Regular Modified Cylindrical Bessel Functions</a>, Up: <a href="Bessel-Functions.html#Bessel-Functions" accesskey="u" rel="up">Bessel Functions</a> &nbsp; [<a href="Function-Index.html#Function-Index" title="Index" rel="index">Index</a>]</p>
</div>
<hr>
<a name="Irregular-Modified-Cylindrical-Bessel-Functions-1"></a>
<h4 class="subsection">7.5.4 Irregular Modified Cylindrical Bessel Functions</h4>
<a name="index-Irregular-Modified-Cylindrical-Bessel-Functions"></a>
<a name="index-K_0028x_0029_002c-Bessel-Functions"></a>

<dl>
<dt><a name="index-gsl_005fsf_005fbessel_005fK0"></a>Function: <em>double</em> <strong>gsl_sf_bessel_K0</strong> <em>(double <var>x</var>)</em></dt>
<dt><a name="index-gsl_005fsf_005fbessel_005fK0_005fe"></a>Function: <em>int</em> <strong>gsl_sf_bessel_K0_e</strong> <em>(double <var>x</var>, gsl_sf_result * <var>result</var>)</em></dt>
<dd><p>These routines compute the irregular modified cylindrical Bessel
function of zeroth order, <em>K_0(x)</em>, for <em>x &gt; 0</em>.
</p></dd></dl>

<dl>
<dt><a name="index-gsl_005fsf_005fbessel_005fK1"></a>Function: <em>double</em> <strong>gsl_sf_bessel_K1</strong> <em>(double <var>x</var>)</em></dt>
<dt><a name="index-gsl_005fsf_005fbessel_005fK1_005fe"></a>Function: <em>int</em> <strong>gsl_sf_bessel_K1_e</strong> <em>(double <var>x</var>, gsl_sf_result * <var>result</var>)</em></dt>
<dd><p>These routines compute the irregular modified cylindrical Bessel
function of first order, <em>K_1(x)</em>, for <em>x &gt; 0</em>.
</p></dd></dl>

<dl>
<dt><a name="index-gsl_005fsf_005fbessel_005fKn"></a>Function: <em>double</em> <strong>gsl_sf_bessel_Kn</strong> <em>(int <var>n</var>, double <var>x</var>)</em></dt>
<dt><a name="index-gsl_005fsf_005fbessel_005fKn_005fe"></a>Function: <em>int</em> <strong>gsl_sf_bessel_Kn_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 irregular modified cylindrical Bessel
function of order <var>n</var>, <em>K_n(x)</em>, for <em>x &gt; 0</em>.
</p></dd></dl>

<dl>
<dt><a name="index-gsl_005fsf_005fbessel_005fKn_005farray"></a>Function: <em>int</em> <strong>gsl_sf_bessel_Kn_array</strong> <em>(int <var>nmin</var>, int <var>nmax</var>, double <var>x</var>, double <var>result_array</var>[])</em></dt>
<dd><p>This routine computes the values of the irregular modified cylindrical
Bessel functions <em>K_n(x)</em> for <em>n</em> from <var>nmin</var> to
<var>nmax</var> inclusive, storing the results in the array
<var>result_array</var>. The start of the range <var>nmin</var> must be positive
or zero. The domain of the function is <em>x&gt;0</em>. The values are
computed using recurrence relations for efficiency, and therefore
may differ slightly from the exact values.
</p></dd></dl>

<dl>
<dt><a name="index-gsl_005fsf_005fbessel_005fK0_005fscaled"></a>Function: <em>double</em> <strong>gsl_sf_bessel_K0_scaled</strong> <em>(double <var>x</var>)</em></dt>
<dt><a name="index-gsl_005fsf_005fbessel_005fK0_005fscaled_005fe"></a>Function: <em>int</em> <strong>gsl_sf_bessel_K0_scaled_e</strong> <em>(double <var>x</var>, gsl_sf_result * <var>result</var>)</em></dt>
<dd><p>These routines compute the scaled irregular modified cylindrical Bessel
function of zeroth order <em>\exp(x) K_0(x)</em> for <em>x&gt;0</em>.
</p></dd></dl>

<dl>
<dt><a name="index-gsl_005fsf_005fbessel_005fK1_005fscaled"></a>Function: <em>double</em> <strong>gsl_sf_bessel_K1_scaled</strong> <em>(double <var>x</var>) </em></dt>
<dt><a name="index-gsl_005fsf_005fbessel_005fK1_005fscaled_005fe"></a>Function: <em>int</em> <strong>gsl_sf_bessel_K1_scaled_e</strong> <em>(double <var>x</var>, gsl_sf_result * <var>result</var>)</em></dt>
<dd><p>These routines compute the scaled irregular modified cylindrical Bessel
function of first order <em>\exp(x) K_1(x)</em> for <em>x&gt;0</em>.
</p></dd></dl>

<dl>
<dt><a name="index-gsl_005fsf_005fbessel_005fKn_005fscaled"></a>Function: <em>double</em> <strong>gsl_sf_bessel_Kn_scaled</strong> <em>(int <var>n</var>, double <var>x</var>)</em></dt>
<dt><a name="index-gsl_005fsf_005fbessel_005fKn_005fscaled_005fe"></a>Function: <em>int</em> <strong>gsl_sf_bessel_Kn_scaled_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 scaled irregular modified cylindrical Bessel
function of order <var>n</var>, <em>\exp(x) K_n(x)</em>, for <em>x&gt;0</em>.
</p></dd></dl>

<dl>
<dt><a name="index-gsl_005fsf_005fbessel_005fKn_005fscaled_005farray"></a>Function: <em>int</em> <strong>gsl_sf_bessel_Kn_scaled_array</strong> <em>(int <var>nmin</var>, int <var>nmax</var>, double <var>x</var>, double <var>result_array</var>[])</em></dt>
<dd><p>This routine computes the values of the scaled irregular cylindrical
Bessel functions <em>\exp(x) K_n(x)</em> for <em>n</em> from <var>nmin</var> to
<var>nmax</var> inclusive, storing the results in the array
<var>result_array</var>. The start of the range <var>nmin</var> must be positive
or zero.  The domain of the function is <em>x&gt;0</em>. The values are
computed using recurrence relations for efficiency, and therefore
may differ slightly from the exact values.
</p></dd></dl>


<hr>
<div class="header">
<p>
Next: <a href="Regular-Spherical-Bessel-Functions.html#Regular-Spherical-Bessel-Functions" accesskey="n" rel="next">Regular Spherical Bessel Functions</a>, Previous: <a href="Regular-Modified-Cylindrical-Bessel-Functions.html#Regular-Modified-Cylindrical-Bessel-Functions" accesskey="p" rel="previous">Regular Modified Cylindrical Bessel Functions</a>, Up: <a href="Bessel-Functions.html#Bessel-Functions" accesskey="u" rel="up">Bessel Functions</a> &nbsp; [<a href="Function-Index.html#Function-Index" title="Index" rel="index">Index</a>]</p>
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