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| <a name="BESSEL_005fYN-_002d_002d_002d-Bessel-function-of-the-second-kind"></a> |
| <h3 class="section">8.32 <code>BESSEL_YN</code> — 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> |
| </dl> |
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