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<title>GNU Scientific Library – Reference Manual: Regular Spherical Bessel Functions</title>
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<a name="Regular-Spherical-Bessel-Functions"></a>
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<p>
Next: <a href="Irregular-Spherical-Bessel-Functions.html#Irregular-Spherical-Bessel-Functions" accesskey="n" rel="next">Irregular Spherical Bessel Functions</a>, Previous: <a href="Irregular-Modified-Cylindrical-Bessel-Functions.html#Irregular-Modified-Cylindrical-Bessel-Functions" accesskey="p" rel="previous">Irregular Modified Cylindrical Bessel Functions</a>, Up: <a href="Bessel-Functions.html#Bessel-Functions" accesskey="u" rel="up">Bessel Functions</a> [<a href="Function-Index.html#Function-Index" title="Index" rel="index">Index</a>]</p>
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<hr>
<a name="Regular-Spherical-Bessel-Functions-1"></a>
<h4 class="subsection">7.5.5 Regular Spherical Bessel Functions</h4>
<a name="index-Spherical-Bessel-Functions"></a>
<a name="index-Regular-Spherical-Bessel-Functions"></a>
<a name="index-j_0028x_0029_002c-Bessel-Functions"></a>
<dl>
<dt><a name="index-gsl_005fsf_005fbessel_005fj0"></a>Function: <em>double</em> <strong>gsl_sf_bessel_j0</strong> <em>(double <var>x</var>)</em></dt>
<dt><a name="index-gsl_005fsf_005fbessel_005fj0_005fe"></a>Function: <em>int</em> <strong>gsl_sf_bessel_j0_e</strong> <em>(double <var>x</var>, gsl_sf_result * <var>result</var>)</em></dt>
<dd><p>These routines compute the regular spherical Bessel function of zeroth
order, <em>j_0(x) = \sin(x)/x</em>.
</p></dd></dl>
<dl>
<dt><a name="index-gsl_005fsf_005fbessel_005fj1"></a>Function: <em>double</em> <strong>gsl_sf_bessel_j1</strong> <em>(double <var>x</var>)</em></dt>
<dt><a name="index-gsl_005fsf_005fbessel_005fj1_005fe"></a>Function: <em>int</em> <strong>gsl_sf_bessel_j1_e</strong> <em>(double <var>x</var>, gsl_sf_result * <var>result</var>)</em></dt>
<dd><p>These routines compute the regular spherical Bessel function of first
order, <em>j_1(x) = (\sin(x)/x - \cos(x))/x</em>.
</p></dd></dl>
<dl>
<dt><a name="index-gsl_005fsf_005fbessel_005fj2"></a>Function: <em>double</em> <strong>gsl_sf_bessel_j2</strong> <em>(double <var>x</var>)</em></dt>
<dt><a name="index-gsl_005fsf_005fbessel_005fj2_005fe"></a>Function: <em>int</em> <strong>gsl_sf_bessel_j2_e</strong> <em>(double <var>x</var>, gsl_sf_result * <var>result</var>)</em></dt>
<dd><p>These routines compute the regular spherical Bessel function of second
order, <em>j_2(x) = ((3/x^2 - 1)\sin(x) - 3\cos(x)/x)/x</em>.
</p></dd></dl>
<dl>
<dt><a name="index-gsl_005fsf_005fbessel_005fjl"></a>Function: <em>double</em> <strong>gsl_sf_bessel_jl</strong> <em>(int <var>l</var>, double <var>x</var>)</em></dt>
<dt><a name="index-gsl_005fsf_005fbessel_005fjl_005fe"></a>Function: <em>int</em> <strong>gsl_sf_bessel_jl_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 regular spherical Bessel function of
order <var>l</var>, <em>j_l(x)</em>, for <em>l >= 0</em> and <em>x >= 0</em>.
</p></dd></dl>
<dl>
<dt><a name="index-gsl_005fsf_005fbessel_005fjl_005farray"></a>Function: <em>int</em> <strong>gsl_sf_bessel_jl_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 regular spherical Bessel
functions <em>j_l(x)</em> for <em>l</em> from 0 to <var>lmax</var>
inclusive for <em>lmax >= 0</em> and <em>x >= 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>
<dl>
<dt><a name="index-gsl_005fsf_005fbessel_005fjl_005fsteed_005farray"></a>Function: <em>int</em> <strong>gsl_sf_bessel_jl_steed_array</strong> <em>(int <var>lmax</var>, double <var>x</var>, double * <var>result_array</var>)</em></dt>
<dd><p>This routine uses Steed’s method to compute the values of the regular
spherical Bessel functions <em>j_l(x)</em> for <em>l</em> from 0 to
<var>lmax</var> inclusive for <em>lmax >= 0</em> and <em>x >= 0</em>, storing the results in the array
<var>result_array</var>.
The Steed/Barnett algorithm is described in <cite>Comp. Phys. Comm.</cite> 21,
297 (1981). Steed’s method is more stable than the
recurrence used in the other functions but is also slower.
</p></dd></dl>
<hr>
<div class="header">
<p>
Next: <a href="Irregular-Spherical-Bessel-Functions.html#Irregular-Spherical-Bessel-Functions" accesskey="n" rel="next">Irregular Spherical Bessel Functions</a>, Previous: <a href="Irregular-Modified-Cylindrical-Bessel-Functions.html#Irregular-Modified-Cylindrical-Bessel-Functions" accesskey="p" rel="previous">Irregular Modified Cylindrical Bessel Functions</a>, Up: <a href="Bessel-Functions.html#Bessel-Functions" accesskey="u" rel="up">Bessel Functions</a> [<a href="Function-Index.html#Function-Index" title="Index" rel="index">Index</a>]</p>
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