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<title>Irregular Modified Spherical Bessel Functions - GNU Scientific Library -- Reference Manual</title>
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<h4 class="subsection">7.5.8 Irregular Modified Spherical Bessel Functions</h4>
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<p><a name="index-Irregular-Modified-Spherical-Bessel-Functions-345"></a>
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The irregular modified spherical Bessel functions k_l(x)
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are related to the irregular modified Bessel functions of fractional order,
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<!-- {$k_l(x) = \sqrt{\pi/(2x)} K_{l+1/2}(x)$} -->
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k_l(x) = \sqrt{\pi/(2x)} K_{l+1/2}(x).
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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-346"></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-347"></a></var><br>
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<blockquote><p>These routines compute the scaled irregular modified spherical 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, GSL_EUNDRFLW -->
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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-348"></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-349"></a></var><br>
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<blockquote><p>These routines compute the scaled irregular modified spherical 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, GSL_EOVRFLW -->
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</p></blockquote></div>
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— Function: double <b>gsl_sf_bessel_k2_scaled</b> (<var>double x</var>)<var><a name="index-gsl_005fsf_005fbessel_005fk2_005fscaled-350"></a></var><br>
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— Function: int <b>gsl_sf_bessel_k2_scaled_e</b> (<var>double x, gsl_sf_result * result</var>)<var><a name="index-gsl_005fsf_005fbessel_005fk2_005fscaled_005fe-351"></a></var><br>
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<blockquote><p>These routines compute the scaled irregular modified spherical Bessel
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function of second order, \exp(x) k_2(x), for x>0.
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<!-- Domain: x > 0.0 -->
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<!-- Exceptional Return Values: GSL_EDOM, GSL_EUNDRFLW, GSL_EOVRFLW -->
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</p></blockquote></div>
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— Function: double <b>gsl_sf_bessel_kl_scaled</b> (<var>int l, double x</var>)<var><a name="index-gsl_005fsf_005fbessel_005fkl_005fscaled-352"></a></var><br>
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— Function: int <b>gsl_sf_bessel_kl_scaled_e</b> (<var>int l, double x, gsl_sf_result * result</var>)<var><a name="index-gsl_005fsf_005fbessel_005fkl_005fscaled_005fe-353"></a></var><br>
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<blockquote><p>These routines compute the scaled irregular modified spherical Bessel
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function of order <var>l</var>, \exp(x) k_l(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_kl_scaled_array</b> (<var>int lmax, double x, double result_array</var>[])<var><a name="index-gsl_005fsf_005fbessel_005fkl_005fscaled_005farray-354"></a></var><br>
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<blockquote><p>This routine computes the values of the scaled irregular modified
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spherical Bessel functions \exp(x) k_l(x) for l from
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0 to <var>lmax</var> inclusive for <!-- {$lmax \geq 0$} -->
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lmax >= 0 and x>0, storing the results in
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the array <var>result_array</var>.
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The values are computed using recurrence relations for
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efficiency, and therefore may differ slightly from the exact values.
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<!-- Domain: lmax >= 0 -->
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<!-- Conditions: l=0,1,...,lmax -->
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<!-- Exceptional Return Values: GSL_EDOM, GSL_EUNDRFLW -->
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</p></blockquote></div>
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