<html lang="en"> <head> <title>BESSEL_YN - The GNU Fortran Compiler</title> <meta http-equiv="Content-Type" content="text/html"> <meta name="description" content="The GNU Fortran Compiler"> <meta name="generator" content="makeinfo 4.13"> <link title="Top" rel="start" href="index.html#Top"> <link rel="up" href="Intrinsic-Procedures.html#Intrinsic-Procedures" title="Intrinsic Procedures"> <link rel="prev" href="BESSEL_005fY1.html#BESSEL_005fY1" title="BESSEL_Y1"> <link rel="next" href="BGE.html#BGE" title="BGE"> <link href="http://www.gnu.org/software/texinfo/" rel="generator-home" title="Texinfo Homepage"> <!-- Copyright (C) 1999, 2000, 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009, 2010, 2011 Free Software Foundation, Inc. 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Copies published by the Free Software Foundation raise funds for GNU development.--> <meta http-equiv="Content-Style-Type" content="text/css"> <style type="text/css"><!-- pre.display { font-family:inherit } pre.format { font-family:inherit } pre.smalldisplay { font-family:inherit; font-size:smaller } pre.smallformat { font-family:inherit; font-size:smaller } pre.smallexample { font-size:smaller } pre.smalllisp { font-size:smaller } span.sc { font-variant:small-caps } span.roman { font-family:serif; font-weight:normal; } span.sansserif { font-family:sans-serif; font-weight:normal; } --></style> </head> <body> <div class="node"> <a name="BESSEL_YN"></a> <a name="BESSEL_005fYN"></a> <p> Next: <a rel="next" accesskey="n" href="BGE.html#BGE">BGE</a>, Previous: <a rel="previous" accesskey="p" href="BESSEL_005fY1.html#BESSEL_005fY1">BESSEL_Y1</a>, Up: <a rel="up" accesskey="u" href="Intrinsic-Procedures.html#Intrinsic-Procedures">Intrinsic Procedures</a> <hr> </div> <h3 class="section">8.29 <code>BESSEL_YN</code> — Bessel function of the second kind</h3> <p><a name="index-BESSEL_005fYN-451"></a><a name="index-BESYN-452"></a><a name="index-DBESYN-453"></a><a name="index-Bessel-function_002c-second-kind-454"></a> <dl> <dt><em>Description</em>:<dd><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><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>. <br><dt><em>Standard</em>:<dd>Fortran 2008 and later, negative <var>N</var> is allowed as GNU extension <br><dt><em>Class</em>:<dd>Elemental function, except for the transformational function <code>BESSEL_YN(N1, N2, X)</code> <br><dt><em>Syntax</em>:<dd> <p><table summary=""><tr align="left"><td valign="top" width="80%"><code>RESULT = BESSEL_YN(N, X)</code> <br></td></tr><tr align="left"><td valign="top" width="80%"><code>RESULT = BESSEL_YN(N1, N2, X)</code> <br></td></tr></table> <br><dt><em>Arguments</em>:<dd> <p><table summary=""><tr align="left"><td valign="top" width="15%"><var>N</var> </td><td valign="top" width="70%">Shall be a scalar or an array of type <code>INTEGER</code> . <br></td></tr><tr align="left"><td valign="top" width="15%"><var>N1</var> </td><td valign="top" width="70%">Shall be a non-negative scalar of type <code>INTEGER</code>. <br></td></tr><tr align="left"><td valign="top" width="15%"><var>N2</var> </td><td valign="top" width="70%">Shall be a non-negative scalar of type <code>INTEGER</code>. <br></td></tr><tr align="left"><td valign="top" width="15%"><var>X</var> </td><td valign="top" 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. <br></td></tr></table> <br><dt><em>Return value</em>:<dd>The return value is a scalar of type <code>REAL</code>. It has the same kind as <var>X</var>. <br><dt><em>Note</em>:<dd>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. <br><dt><em>Example</em>:<dd> <pre class="smallexample"> program test_besyn real(8) :: x = 1.0_8 x = bessel_yn(5,x) end program test_besyn </pre> <br><dt><em>Specific names</em>:<dd> <p><table summary=""><tr align="left"><td valign="top" width="20%">Name </td><td valign="top" width="20%">Argument </td><td valign="top" width="20%">Return type </td><td valign="top" width="25%">Standard <br></td></tr><tr align="left"><td valign="top" width="20%"><code>DBESYN(N,X)</code> </td><td valign="top" width="20%"><code>INTEGER N</code> </td><td valign="top" width="20%"><code>REAL(8)</code> </td><td valign="top" width="25%">GNU extension <br></td></tr><tr align="left"><td valign="top" width="20%"></td><td valign="top" width="20%"><code>REAL(8) X</code> </td><td valign="top" width="20%"></td><td valign="top" width="25%"> <br></td></tr></table> </dl> </body></html>