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

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<a name="Irregular-Spherical-Bessel-Functions"></a>
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<p>
Next: <a href="Regular-Modified-Spherical-Bessel-Functions.html#Regular-Modified-Spherical-Bessel-Functions" accesskey="n" rel="next">Regular Modified Spherical Bessel Functions</a>, Previous: <a href="Regular-Spherical-Bessel-Functions.html#Regular-Spherical-Bessel-Functions" accesskey="p" rel="previous">Regular 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>
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<hr>
<a name="Irregular-Spherical-Bessel-Functions-1"></a>
<h4 class="subsection">7.5.6 Irregular Spherical Bessel Functions</h4>
<a name="index-Irregular-Spherical-Bessel-Functions"></a>
<a name="index-y_0028x_0029_002c-Bessel-Functions"></a>

<dl>
<dt><a name="index-gsl_005fsf_005fbessel_005fy0"></a>Function: <em>double</em> <strong>gsl_sf_bessel_y0</strong> <em>(double <var>x</var>)</em></dt>
<dt><a name="index-gsl_005fsf_005fbessel_005fy0_005fe"></a>Function: <em>int</em> <strong>gsl_sf_bessel_y0_e</strong> <em>(double <var>x</var>, gsl_sf_result * <var>result</var>)</em></dt>
<dd><p>These routines compute the irregular spherical Bessel function of zeroth
order, <em>y_0(x) = -\cos(x)/x</em>.
</p></dd></dl>

<dl>
<dt><a name="index-gsl_005fsf_005fbessel_005fy1"></a>Function: <em>double</em> <strong>gsl_sf_bessel_y1</strong> <em>(double <var>x</var>)</em></dt>
<dt><a name="index-gsl_005fsf_005fbessel_005fy1_005fe"></a>Function: <em>int</em> <strong>gsl_sf_bessel_y1_e</strong> <em>(double <var>x</var>, gsl_sf_result * <var>result</var>)</em></dt>
<dd><p>These routines compute the irregular spherical Bessel function of first
order, <em>y_1(x) = -(\cos(x)/x + \sin(x))/x</em>.
</p></dd></dl>

<dl>
<dt><a name="index-gsl_005fsf_005fbessel_005fy2"></a>Function: <em>double</em> <strong>gsl_sf_bessel_y2</strong> <em>(double <var>x</var>)</em></dt>
<dt><a name="index-gsl_005fsf_005fbessel_005fy2_005fe"></a>Function: <em>int</em> <strong>gsl_sf_bessel_y2_e</strong> <em>(double <var>x</var>, gsl_sf_result * <var>result</var>)</em></dt>
<dd><p>These routines compute the irregular spherical Bessel function of second
order, <em>y_2(x) = (-3/x^3 + 1/x)\cos(x) - (3/x^2)\sin(x)</em>.
</p></dd></dl>

<dl>
<dt><a name="index-gsl_005fsf_005fbessel_005fyl"></a>Function: <em>double</em> <strong>gsl_sf_bessel_yl</strong> <em>(int <var>l</var>, double <var>x</var>)</em></dt>
<dt><a name="index-gsl_005fsf_005fbessel_005fyl_005fe"></a>Function: <em>int</em> <strong>gsl_sf_bessel_yl_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 irregular spherical Bessel function of 
order <var>l</var>, <em>y_l(x)</em>, for <em>l &gt;= 0</em>.
</p></dd></dl>

<dl>
<dt><a name="index-gsl_005fsf_005fbessel_005fyl_005farray"></a>Function: <em>int</em> <strong>gsl_sf_bessel_yl_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 irregular spherical Bessel
functions <em>y_l(x)</em> for <em>l</em> from 0 to <var>lmax</var>
inclusive  for <em>lmax &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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