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<a name="Irregular-Modified-Cylindrical-Bessel-Functions"></a>
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<h4 class="subsection">7.5.4 Irregular Modified Cylindrical Bessel Functions</h4>
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<p><a name="index-Irregular-Modified-Cylindrical-Bessel-Functions-297"></a>
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— Function: double <b>gsl_sf_bessel_K0</b> (<var>double x</var>)<var><a name="index-gsl_005fsf_005fbessel_005fK0-298"></a></var><br>
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— Function: int <b>gsl_sf_bessel_K0_e</b> (<var>double x, gsl_sf_result * result</var>)<var><a name="index-gsl_005fsf_005fbessel_005fK0_005fe-299"></a></var><br>
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<blockquote><p>These routines compute the irregular modified cylindrical Bessel
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function of zeroth order, K_0(x), for x > 0.
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<!-- Domain: x > 0.0 -->
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<!-- Exceptional Return Values: GSL_EDOM, GSL_EUNDRFLW -->
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</p></blockquote></div>
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— Function: double <b>gsl_sf_bessel_K1</b> (<var>double x</var>)<var><a name="index-gsl_005fsf_005fbessel_005fK1-300"></a></var><br>
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— Function: int <b>gsl_sf_bessel_K1_e</b> (<var>double x, gsl_sf_result * result</var>)<var><a name="index-gsl_005fsf_005fbessel_005fK1_005fe-301"></a></var><br>
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<blockquote><p>These routines compute the irregular modified cylindrical Bessel
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function of first order, K_1(x), for x > 0.
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<!-- Domain: x > 0.0 -->
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<!-- Exceptional Return Values: GSL_EDOM, GSL_EOVRFLW, GSL_EUNDRFLW -->
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</p></blockquote></div>
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— Function: double <b>gsl_sf_bessel_Kn</b> (<var>int n, double x</var>)<var><a name="index-gsl_005fsf_005fbessel_005fKn-302"></a></var><br>
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— Function: int <b>gsl_sf_bessel_Kn_e</b> (<var>int n, double x, gsl_sf_result * result</var>)<var><a name="index-gsl_005fsf_005fbessel_005fKn_005fe-303"></a></var><br>
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<blockquote><p>These routines compute the irregular modified cylindrical Bessel
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function of order <var>n</var>, K_n(x), for x > 0.
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<!-- Domain: x > 0.0 -->
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<!-- Exceptional Return Values: GSL_EDOM, GSL_EOVRFLW, GSL_EUNDRFLW -->
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</p></blockquote></div>
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— Function: int <b>gsl_sf_bessel_Kn_array</b> (<var>int nmin, int nmax, double x, double result_array</var>[])<var><a name="index-gsl_005fsf_005fbessel_005fKn_005farray-304"></a></var><br>
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<blockquote><p>This routine computes the values of the irregular modified cylindrical
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Bessel functions K_n(x) for n from <var>nmin</var> to
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<var>nmax</var> inclusive, storing the results in the array
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<var>result_array</var>. The start of the range <var>nmin</var> must be positive
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or zero. The domain of the function is x>0. The values are
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computed using recurrence relations for efficiency, and therefore
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may differ slightly from the exact values.
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<!-- Conditions: n=nmin,...,nmax -->
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<!-- Domain: x > 0.0, nmin>=0, nmax >= nmin -->
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<!-- Exceptional Return Values: GSL_EDOM, GSL_EOVRFLW, GSL_EUNDRFLW -->
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</p></blockquote></div>
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— Function: double <b>gsl_sf_bessel_K0_scaled</b> (<var>double x</var>)<var><a name="index-gsl_005fsf_005fbessel_005fK0_005fscaled-305"></a></var><br>
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— Function: int <b>gsl_sf_bessel_K0_scaled_e</b> (<var>double x, gsl_sf_result * result</var>)<var><a name="index-gsl_005fsf_005fbessel_005fK0_005fscaled_005fe-306"></a></var><br>
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<blockquote><p>These routines compute the scaled irregular modified cylindrical Bessel
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function of zeroth order \exp(x) K_0(x) for x>0.
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<!-- Domain: x > 0.0 -->
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<!-- Exceptional Return Values: GSL_EDOM -->
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</p></blockquote></div>
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— Function: double <b>gsl_sf_bessel_K1_scaled</b> (<var>double x</var>)<var><a name="index-gsl_005fsf_005fbessel_005fK1_005fscaled-307"></a></var><br>
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— Function: int <b>gsl_sf_bessel_K1_scaled_e</b> (<var>double x, gsl_sf_result * result</var>)<var><a name="index-gsl_005fsf_005fbessel_005fK1_005fscaled_005fe-308"></a></var><br>
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<blockquote><p>These routines compute the scaled irregular modified cylindrical Bessel
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function of first order \exp(x) K_1(x) for x>0.
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<!-- Domain: x > 0.0 -->
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<!-- Exceptional Return Values: GSL_EDOM, GSL_EUNDRFLW -->
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</p></blockquote></div>
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— Function: double <b>gsl_sf_bessel_Kn_scaled</b> (<var>int n, double x</var>)<var><a name="index-gsl_005fsf_005fbessel_005fKn_005fscaled-309"></a></var><br>
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— Function: int <b>gsl_sf_bessel_Kn_scaled_e</b> (<var>int n, double x, gsl_sf_result * result</var>)<var><a name="index-gsl_005fsf_005fbessel_005fKn_005fscaled_005fe-310"></a></var><br>
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<blockquote><p>These routines compute the scaled irregular modified cylindrical Bessel
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function of order <var>n</var>, \exp(x) K_n(x), for x>0.
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<!-- Domain: x > 0.0 -->
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<!-- Exceptional Return Values: GSL_EDOM, GSL_EUNDRFLW -->
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</p></blockquote></div>
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— Function: int <b>gsl_sf_bessel_Kn_scaled_array</b> (<var>int nmin, int nmax, double x, double result_array</var>[])<var><a name="index-gsl_005fsf_005fbessel_005fKn_005fscaled_005farray-311"></a></var><br>
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<blockquote><p>This routine computes the values of the scaled irregular cylindrical
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Bessel functions \exp(x) K_n(x) for n from <var>nmin</var> to
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<var>nmax</var> inclusive, storing the results in the array
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<var>result_array</var>. The start of the range <var>nmin</var> must be positive
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or zero. The domain of the function is x>0. The values are
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computed using recurrence relations for efficiency, and therefore
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may differ slightly from the exact values.
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<!-- Domain: x > 0.0, nmin >=0, nmax >= nmin -->
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<!-- Conditions: n=nmin,...,nmax -->
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<!-- Exceptional Return Values: GSL_EDOM, GSL_EUNDRFLW -->
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</p></blockquote></div>
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