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

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<a name="Regular-Modified-Cylindrical-Bessel-Functions"></a>
<div class="header">
<p>
Next: <a href="Irregular-Modified-Cylindrical-Bessel-Functions.html#Irregular-Modified-Cylindrical-Bessel-Functions" accesskey="n" rel="next">Irregular Modified Cylindrical Bessel Functions</a>, Previous: <a href="Irregular-Cylindrical-Bessel-Functions.html#Irregular-Cylindrical-Bessel-Functions" accesskey="p" rel="previous">Irregular 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="Regular-Modified-Cylindrical-Bessel-Functions-1"></a>
<h4 class="subsection">7.5.3 Regular Modified Cylindrical Bessel Functions</h4>
<a name="index-Modified-Cylindrical-Bessel-Functions"></a>
<a name="index-Regular-Modified-Cylindrical-Bessel-Functions"></a>
<a name="index-I_0028x_0029_002c-Bessel-Functions"></a>

<dl>
<dt><a name="index-gsl_005fsf_005fbessel_005fI0"></a>Function: <em>double</em> <strong>gsl_sf_bessel_I0</strong> <em>(double <var>x</var>)</em></dt>
<dt><a name="index-gsl_005fsf_005fbessel_005fI0_005fe"></a>Function: <em>int</em> <strong>gsl_sf_bessel_I0_e</strong> <em>(double <var>x</var>, gsl_sf_result * <var>result</var>)</em></dt>
<dd><p>These routines compute the regular modified cylindrical Bessel function
of zeroth order, <em>I_0(x)</em>.
</p></dd></dl>

<dl>
<dt><a name="index-gsl_005fsf_005fbessel_005fI1"></a>Function: <em>double</em> <strong>gsl_sf_bessel_I1</strong> <em>(double <var>x</var>)</em></dt>
<dt><a name="index-gsl_005fsf_005fbessel_005fI1_005fe"></a>Function: <em>int</em> <strong>gsl_sf_bessel_I1_e</strong> <em>(double <var>x</var>, gsl_sf_result * <var>result</var>)</em></dt>
<dd><p>These routines compute the regular modified cylindrical Bessel function
of first order, <em>I_1(x)</em>.
</p></dd></dl>

<dl>
<dt><a name="index-gsl_005fsf_005fbessel_005fIn"></a>Function: <em>double</em> <strong>gsl_sf_bessel_In</strong> <em>(int <var>n</var>, double <var>x</var>)</em></dt>
<dt><a name="index-gsl_005fsf_005fbessel_005fIn_005fe"></a>Function: <em>int</em> <strong>gsl_sf_bessel_In_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 regular modified cylindrical Bessel function
of order <var>n</var>, <em>I_n(x)</em>.
</p></dd></dl>

<dl>
<dt><a name="index-gsl_005fsf_005fbessel_005fIn_005farray"></a>Function: <em>int</em> <strong>gsl_sf_bessel_In_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 regular modified cylindrical
Bessel functions <em>I_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 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_005fI0_005fscaled"></a>Function: <em>double</em> <strong>gsl_sf_bessel_I0_scaled</strong> <em>(double <var>x</var>)</em></dt>
<dt><a name="index-gsl_005fsf_005fbessel_005fI0_005fscaled_005fe"></a>Function: <em>int</em> <strong>gsl_sf_bessel_I0_scaled_e</strong> <em>(double <var>x</var>, gsl_sf_result * <var>result</var>)</em></dt>
<dd><p>These routines compute the scaled regular modified cylindrical Bessel
function of zeroth order <em>\exp(-|x|) I_0(x)</em>.
</p></dd></dl>

<dl>
<dt><a name="index-gsl_005fsf_005fbessel_005fI1_005fscaled"></a>Function: <em>double</em> <strong>gsl_sf_bessel_I1_scaled</strong> <em>(double <var>x</var>)</em></dt>
<dt><a name="index-gsl_005fsf_005fbessel_005fI1_005fscaled_005fe"></a>Function: <em>int</em> <strong>gsl_sf_bessel_I1_scaled_e</strong> <em>(double <var>x</var>, gsl_sf_result * <var>result</var>)</em></dt>
<dd><p>These routines compute the scaled regular modified cylindrical Bessel
function of first order <em>\exp(-|x|) I_1(x)</em>.
</p></dd></dl>

<dl>
<dt><a name="index-gsl_005fsf_005fbessel_005fIn_005fscaled"></a>Function: <em>double</em> <strong>gsl_sf_bessel_In_scaled</strong> <em>(int <var>n</var>, double <var>x</var>)</em></dt>
<dt><a name="index-gsl_005fsf_005fbessel_005fIn_005fscaled_005fe"></a>Function: <em>int</em> <strong>gsl_sf_bessel_In_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 regular modified cylindrical Bessel
function of order <var>n</var>, <em>\exp(-|x|) I_n(x)</em> 
</p></dd></dl>

<dl>
<dt><a name="index-gsl_005fsf_005fbessel_005fIn_005fscaled_005farray"></a>Function: <em>int</em> <strong>gsl_sf_bessel_In_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 regular cylindrical
Bessel functions <em>\exp(-|x|) I_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 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="Irregular-Modified-Cylindrical-Bessel-Functions.html#Irregular-Modified-Cylindrical-Bessel-Functions" accesskey="n" rel="next">Irregular Modified Cylindrical Bessel Functions</a>, Previous: <a href="Irregular-Cylindrical-Bessel-Functions.html#Irregular-Cylindrical-Bessel-Functions" accesskey="p" rel="previous">Irregular 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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