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<title>Regular Modified Cylindrical Bessel Functions - GNU Scientific Library -- Reference Manual</title>
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<h4 class="subsection">7.5.3 Regular Modified Cylindrical Bessel Functions</h4>
<p><a name="index-Modified-Cylindrical-Bessel-Functions-300"></a><a name="index-Regular-Modified-Cylindrical-Bessel-Functions-301"></a><a name="index-I_0028x_0029_002c-Bessel-Functions-302"></a>
<div class="defun">
— Function: double <b>gsl_sf_bessel_I0</b> (<var>double x</var>)<var><a name="index-gsl_005fsf_005fbessel_005fI0-303"></a></var><br>
— Function: int <b>gsl_sf_bessel_I0_e</b> (<var>double x, gsl_sf_result * result</var>)<var><a name="index-gsl_005fsf_005fbessel_005fI0_005fe-304"></a></var><br>
<blockquote><p>These routines compute the regular modified cylindrical Bessel function
of zeroth order, I_0(x).
<!-- Exceptional Return Values: GSL_EOVRFLW -->
</p></blockquote></div>
<div class="defun">
— Function: double <b>gsl_sf_bessel_I1</b> (<var>double x</var>)<var><a name="index-gsl_005fsf_005fbessel_005fI1-305"></a></var><br>
— Function: int <b>gsl_sf_bessel_I1_e</b> (<var>double x, gsl_sf_result * result</var>)<var><a name="index-gsl_005fsf_005fbessel_005fI1_005fe-306"></a></var><br>
<blockquote><p>These routines compute the regular modified cylindrical Bessel function
of first order, I_1(x).
<!-- Exceptional Return Values: GSL_EOVRFLW, GSL_EUNDRFLW -->
</p></blockquote></div>
<div class="defun">
— Function: double <b>gsl_sf_bessel_In</b> (<var>int n, double x</var>)<var><a name="index-gsl_005fsf_005fbessel_005fIn-307"></a></var><br>
— Function: int <b>gsl_sf_bessel_In_e</b> (<var>int n, double x, gsl_sf_result * result</var>)<var><a name="index-gsl_005fsf_005fbessel_005fIn_005fe-308"></a></var><br>
<blockquote><p>These routines compute the regular modified cylindrical Bessel function
of order <var>n</var>, I_n(x).
<!-- Exceptional Return Values: GSL_EOVRFLW, GSL_EUNDRFLW -->
</p></blockquote></div>
<div class="defun">
— Function: int <b>gsl_sf_bessel_In_array</b> (<var>int nmin, int nmax, double x, double result_array</var>[])<var><a name="index-gsl_005fsf_005fbessel_005fIn_005farray-309"></a></var><br>
<blockquote><p>This routine computes the values of the regular modified cylindrical
Bessel functions I_n(x) for n 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.
<!-- Domain: nmin >=0, nmax >= nmin -->
<!-- Conditions: n=nmin,...,nmax, nmin >=0, nmax >= nmin -->
<!-- Exceptional Return Values: GSL_EDOM, GSL_EOVRFLW, GSL_EUNDRFLW -->
</p></blockquote></div>
<div class="defun">
— Function: double <b>gsl_sf_bessel_I0_scaled</b> (<var>double x</var>)<var><a name="index-gsl_005fsf_005fbessel_005fI0_005fscaled-310"></a></var><br>
— Function: int <b>gsl_sf_bessel_I0_scaled_e</b> (<var>double x, gsl_sf_result * result</var>)<var><a name="index-gsl_005fsf_005fbessel_005fI0_005fscaled_005fe-311"></a></var><br>
<blockquote><p>These routines compute the scaled regular modified cylindrical Bessel
function of zeroth order \exp(-|x|) I_0(x).
<!-- Exceptional Return Values: none -->
</p></blockquote></div>
<div class="defun">
— Function: double <b>gsl_sf_bessel_I1_scaled</b> (<var>double x</var>)<var><a name="index-gsl_005fsf_005fbessel_005fI1_005fscaled-312"></a></var><br>
— Function: int <b>gsl_sf_bessel_I1_scaled_e</b> (<var>double x, gsl_sf_result * result</var>)<var><a name="index-gsl_005fsf_005fbessel_005fI1_005fscaled_005fe-313"></a></var><br>
<blockquote><p>These routines compute the scaled regular modified cylindrical Bessel
function of first order \exp(-|x|) I_1(x).
<!-- Exceptional Return Values: GSL_EUNDRFLW -->
</p></blockquote></div>
<div class="defun">
— Function: double <b>gsl_sf_bessel_In_scaled</b> (<var>int n, double x</var>)<var><a name="index-gsl_005fsf_005fbessel_005fIn_005fscaled-314"></a></var><br>
— Function: int <b>gsl_sf_bessel_In_scaled_e</b> (<var>int n, double x, gsl_sf_result * result</var>)<var><a name="index-gsl_005fsf_005fbessel_005fIn_005fscaled_005fe-315"></a></var><br>
<blockquote><p>These routines compute the scaled regular modified cylindrical Bessel
function of order <var>n</var>, \exp(-|x|) I_n(x)
<!-- Exceptional Return Values: GSL_EUNDRFLW -->
</p></blockquote></div>
<div class="defun">
— Function: int <b>gsl_sf_bessel_In_scaled_array</b> (<var>int nmin, int nmax, double x, double result_array</var>[])<var><a name="index-gsl_005fsf_005fbessel_005fIn_005fscaled_005farray-316"></a></var><br>
<blockquote><p>This routine computes the values of the scaled regular cylindrical
Bessel functions \exp(-|x|) I_n(x) for n 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.
<!-- Domain: nmin >=0, nmax >= nmin -->
<!-- Conditions: n=nmin,...,nmax -->
<!-- Exceptional Return Values: GSL_EUNDRFLW -->
</p></blockquote></div>
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