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<title>Irregular Modified Cylindrical Bessel Functions - GNU Scientific Library -- Reference Manual</title>
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Previous: <a rel="previous" accesskey="p" href="Regular-Modified-Cylindrical-Bessel-Functions.html">Regular Modified Cylindrical Bessel Functions</a>,
Up: <a rel="up" accesskey="u" href="Bessel-Functions.html">Bessel Functions</a>
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<h4 class="subsection">7.5.4 Irregular Modified Cylindrical Bessel Functions</h4>
<p><a name="index-Irregular-Modified-Cylindrical-Bessel-Functions-318"></a><a name="index-K_0028x_0029_002c-Bessel-Functions-319"></a>
<div class="defun">
— Function: double <b>gsl_sf_bessel_K0</b> (<var>double x</var>)<var><a name="index-gsl_005fsf_005fbessel_005fK0-320"></a></var><br>
— 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-321"></a></var><br>
<blockquote><p>These routines compute the irregular modified cylindrical Bessel
function of zeroth order, K_0(x), for x > 0.
<!-- Domain: x > 0.0 -->
<!-- Exceptional Return Values: GSL_EDOM, GSL_EUNDRFLW -->
</p></blockquote></div>
<div class="defun">
— Function: double <b>gsl_sf_bessel_K1</b> (<var>double x</var>)<var><a name="index-gsl_005fsf_005fbessel_005fK1-322"></a></var><br>
— 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-323"></a></var><br>
<blockquote><p>These routines compute the irregular modified cylindrical Bessel
function of first order, K_1(x), for x > 0.
<!-- Domain: x > 0.0 -->
<!-- Exceptional Return Values: GSL_EDOM, GSL_EOVRFLW, GSL_EUNDRFLW -->
</p></blockquote></div>
<div class="defun">
— Function: double <b>gsl_sf_bessel_Kn</b> (<var>int n, double x</var>)<var><a name="index-gsl_005fsf_005fbessel_005fKn-324"></a></var><br>
— 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-325"></a></var><br>
<blockquote><p>These routines compute the irregular modified cylindrical Bessel
function of order <var>n</var>, K_n(x), for x > 0.
<!-- Domain: x > 0.0 -->
<!-- Exceptional Return Values: GSL_EDOM, GSL_EOVRFLW, GSL_EUNDRFLW -->
</p></blockquote></div>
<div class="defun">
— 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-326"></a></var><br>
<blockquote><p>This routine computes the values of the irregular modified cylindrical
Bessel functions K_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 domain of the function is x>0. The values are
computed using recurrence relations for efficiency, and therefore
may differ slightly from the exact values.
<!-- Conditions: n=nmin,...,nmax -->
<!-- Domain: x > 0.0, 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_K0_scaled</b> (<var>double x</var>)<var><a name="index-gsl_005fsf_005fbessel_005fK0_005fscaled-327"></a></var><br>
— 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-328"></a></var><br>
<blockquote><p>These routines compute the scaled irregular modified cylindrical Bessel
function of zeroth order \exp(x) K_0(x) for x>0.
<!-- Domain: x > 0.0 -->
<!-- Exceptional Return Values: GSL_EDOM -->
</p></blockquote></div>
<div class="defun">
— Function: double <b>gsl_sf_bessel_K1_scaled</b> (<var>double x</var>)<var><a name="index-gsl_005fsf_005fbessel_005fK1_005fscaled-329"></a></var><br>
— 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-330"></a></var><br>
<blockquote><p>These routines compute the scaled irregular modified cylindrical Bessel
function of first order \exp(x) K_1(x) for x>0.
<!-- Domain: x > 0.0 -->
<!-- Exceptional Return Values: GSL_EDOM, GSL_EUNDRFLW -->
</p></blockquote></div>
<div class="defun">
— Function: double <b>gsl_sf_bessel_Kn_scaled</b> (<var>int n, double x</var>)<var><a name="index-gsl_005fsf_005fbessel_005fKn_005fscaled-331"></a></var><br>
— 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-332"></a></var><br>
<blockquote><p>These routines compute the scaled irregular modified cylindrical Bessel
function of order <var>n</var>, \exp(x) K_n(x), for x>0.
<!-- Domain: x > 0.0 -->
<!-- Exceptional Return Values: GSL_EDOM, GSL_EUNDRFLW -->
</p></blockquote></div>
<div class="defun">
— 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-333"></a></var><br>
<blockquote><p>This routine computes the values of the scaled irregular cylindrical
Bessel functions \exp(x) K_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 domain of the function is x>0. The values are
computed using recurrence relations for efficiency, and therefore
may differ slightly from the exact values.
<!-- Domain: x > 0.0, nmin >=0, nmax >= nmin -->
<!-- Conditions: n=nmin,...,nmax -->
<!-- Exceptional Return Values: GSL_EDOM, GSL_EUNDRFLW -->
</p></blockquote></div>
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