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<title>The GNU Fortran Compiler: BESSEL_YN</title>

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<a name="BESSEL_005fYN-_002d_002d_002d-Bessel-function-of-the-second-kind"></a>
<h3 class="section">9.45 <code>BESSEL_YN</code> &mdash; Bessel function of the second kind</h3>
<a name="index-BESSEL_005fYN"></a>
<a name="index-BESYN"></a>
<a name="index-DBESYN"></a>
<a name="index-Bessel-function_002c-second-kind-2"></a>

<dl compact="compact">
<dt><em>Description</em>:</dt>
<dd><p><code>BESSEL_YN(N, X)</code> computes the Bessel function of the second kind of
order <var>N</var> of <var>X</var>. This function is available under the name
<code>BESYN</code> as a GNU extension.  If <var>N</var> and <var>X</var> are arrays,
their ranks and shapes shall conform.  
</p>
<p><code>BESSEL_YN(N1, N2, X)</code> returns an array with the Bessel functions
of the first kind of the orders <var>N1</var> to <var>N2</var>.
</p>
</dd>
<dt><em>Standard</em>:</dt>
<dd><p>Fortran 2008 and later, negative <var>N</var> is allowed as GNU extension
</p>
</dd>
<dt><em>Class</em>:</dt>
<dd><p>Elemental function, except for the transformational function
<code>BESSEL_YN(N1, N2, X)</code>
</p>
</dd>
<dt><em>Syntax</em>:</dt>
<dd><table>
<tr><td width="80%"><code>RESULT = BESSEL_YN(N, X)</code></td></tr>
<tr><td width="80%"><code>RESULT = BESSEL_YN(N1, N2, X)</code></td></tr>
</table>

</dd>
<dt><em>Arguments</em>:</dt>
<dd><table>
<tr><td width="15%"><var>N</var></td><td width="70%">Shall be a scalar or an array of type  <code>INTEGER</code> .</td></tr>
<tr><td width="15%"><var>N1</var></td><td width="70%">Shall be a non-negative scalar of type  <code>INTEGER</code>.</td></tr>
<tr><td width="15%"><var>N2</var></td><td width="70%">Shall be a non-negative scalar of type  <code>INTEGER</code>.</td></tr>
<tr><td width="15%"><var>X</var></td><td width="70%">Shall be a scalar or an array of type  <code>REAL</code>;
for <code>BESSEL_YN(N1, N2, X)</code> it shall be scalar.</td></tr>
</table>

</dd>
<dt><em>Return value</em>:</dt>
<dd><p>The return value is a scalar of type <code>REAL</code>. It has the same
kind as <var>X</var>.
</p>
</dd>
<dt><em>Note</em>:</dt>
<dd><p>The transformational function uses a recurrence algorithm which might,
for some values of <var>X</var>, lead to different results than calls to
the elemental function.
</p>
</dd>
<dt><em>Example</em>:</dt>
<dd><div class="smallexample">
<pre class="smallexample">program test_besyn
  real(8) :: x = 1.0_8
  x = bessel_yn(5,x)
end program test_besyn
</pre></div>

</dd>
<dt><em>Specific names</em>:</dt>
<dd><table>
<tr><td width="20%">Name</td><td width="20%">Argument</td><td width="20%">Return type</td><td width="25%">Standard</td></tr>
<tr><td width="20%"><code>DBESYN(N,X)</code></td><td width="20%"><code>INTEGER N</code></td><td width="20%"><code>REAL(8)</code></td><td width="25%">GNU extension</td></tr>
<tr><td width="20%"></td><td width="20%"><code>REAL(8) X</code></td><td width="20%"></td><td width="25%"></td></tr>
</table>
</dd>
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