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

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<a name="Irregular-Modified-Spherical-Bessel-Functions"></a>
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<p>
Next: <a href="Regular-Bessel-Function-_002d-Fractional-Order.html#Regular-Bessel-Function-_002d-Fractional-Order" accesskey="n" rel="next">Regular Bessel Function - Fractional Order</a>, Previous: <a href="Regular-Modified-Spherical-Bessel-Functions.html#Regular-Modified-Spherical-Bessel-Functions" accesskey="p" rel="previous">Regular Modified Spherical 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-Spherical-Bessel-Functions-1"></a>
<h4 class="subsection">7.5.8 Irregular Modified Spherical Bessel Functions</h4>
<a name="index-Irregular-Modified-Spherical-Bessel-Functions"></a>
<a name="index-k_0028x_0029_002c-Bessel-Functions"></a>

<p>The irregular modified spherical Bessel functions <em>k_l(x)</em>
are related to the irregular modified Bessel functions of fractional order,
<em>k_l(x) = \sqrt{\pi/(2x)} K_{l+1/2}(x)</em>.
</p>
<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 spherical 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 spherical 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_005fk2_005fscaled"></a>Function: <em>double</em> <strong>gsl_sf_bessel_k2_scaled</strong> <em>(double <var>x</var>)</em></dt>
<dt><a name="index-gsl_005fsf_005fbessel_005fk2_005fscaled_005fe"></a>Function: <em>int</em> <strong>gsl_sf_bessel_k2_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 spherical Bessel
function of second order, <em>\exp(x) k_2(x)</em>, for <em>x&gt;0</em>.
</p></dd></dl>

<dl>
<dt><a name="index-gsl_005fsf_005fbessel_005fkl_005fscaled"></a>Function: <em>double</em> <strong>gsl_sf_bessel_kl_scaled</strong> <em>(int <var>l</var>, double <var>x</var>)</em></dt>
<dt><a name="index-gsl_005fsf_005fbessel_005fkl_005fscaled_005fe"></a>Function: <em>int</em> <strong>gsl_sf_bessel_kl_scaled_e</strong> <em>(int <var>l</var>, double <var>x</var>, gsl_sf_result * <var>result</var>)</em></dt>
<dd><p>These routines compute the scaled irregular modified spherical Bessel
function of order <var>l</var>, <em>\exp(x) k_l(x)</em>, for <em>x&gt;0</em>.
</p></dd></dl>

<dl>
<dt><a name="index-gsl_005fsf_005fbessel_005fkl_005fscaled_005farray"></a>Function: <em>int</em> <strong>gsl_sf_bessel_kl_scaled_array</strong> <em>(int <var>lmax</var>, double <var>x</var>, double <var>result_array</var>[])</em></dt>
<dd><p>This routine computes the values of the scaled irregular modified
spherical Bessel functions <em>\exp(x) k_l(x)</em> for <em>l</em> from
0 to <var>lmax</var> inclusive for <em>lmax &gt;= 0</em> and <em>x&gt;0</em>, storing the results in
the array <var>result_array</var>. 
The values are computed using recurrence relations for
efficiency, and therefore may differ slightly from the exact values.
</p></dd></dl>





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