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<H2>

cern.jet.math
 
Class Bessel</H2>
<PRE>
<A HREF="http://java.sun.com/j2se/1.4/docs/api/java/lang/Object.html" title="class or interface in java.lang">java.lang.Object</A>
 <IMG SRC="../../../resources/inherit.gif" ALT="extended by"><A HREF="../../../cern/jet/math/Constants.html" title="class in cern.jet.math">cern.jet.math.Constants</A>
 <IMG SRC="../../../resources/inherit.gif" ALT="extended by">cern.jet.math.Bessel
</PRE>
<HR>
<DL>
<DT>public class Bessel<DT>extends <A HREF="../../../cern/jet/math/Constants.html" title="class in cern.jet.math">Constants</A></DL>

Bessel and Airy functions.

<HR>

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Method Summary</TD>
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<CODE>static&nbsp;double</CODE></TD>
<TD><CODE><A HREF="../../../cern/jet/math/Bessel.html#i0(double)">i0</A>(double&nbsp;x)</CODE>

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Returns the modified Bessel function of order 0 of the
 argument.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%">
<CODE>static&nbsp;double</CODE></TD>
<TD><CODE><A HREF="../../../cern/jet/math/Bessel.html#i0e(double)">i0e</A>(double&nbsp;x)</CODE>

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Returns the exponentially scaled modified Bessel function
 of order 0 of the argument.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%">
<CODE>static&nbsp;double</CODE></TD>
<TD><CODE><A HREF="../../../cern/jet/math/Bessel.html#i1(double)">i1</A>(double&nbsp;x)</CODE>

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Returns the modified Bessel function of order 1 of the
 argument.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%">
<CODE>static&nbsp;double</CODE></TD>
<TD><CODE><A HREF="../../../cern/jet/math/Bessel.html#i1e(double)">i1e</A>(double&nbsp;x)</CODE>

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Returns the exponentially scaled modified Bessel function
 of order 1 of the argument.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%">
<CODE>static&nbsp;double</CODE></TD>
<TD><CODE><A HREF="../../../cern/jet/math/Bessel.html#j0(double)">j0</A>(double&nbsp;x)</CODE>

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Returns the Bessel function of the first kind of order 0 of the argument.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%">
<CODE>static&nbsp;double</CODE></TD>
<TD><CODE><A HREF="../../../cern/jet/math/Bessel.html#j1(double)">j1</A>(double&nbsp;x)</CODE>

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Returns the Bessel function of the first kind of order 1 of the argument.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%">
<CODE>static&nbsp;double</CODE></TD>
<TD><CODE><A HREF="../../../cern/jet/math/Bessel.html#jn(int, double)">jn</A>(int&nbsp;n,
 double&nbsp;x)</CODE>

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Returns the Bessel function of the first kind of order <tt>n</tt> of the argument.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%">
<CODE>static&nbsp;double</CODE></TD>
<TD><CODE><A HREF="../../../cern/jet/math/Bessel.html#k0(double)">k0</A>(double&nbsp;x)</CODE>

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Returns the modified Bessel function of the third kind
 of order 0 of the argument.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%">
<CODE>static&nbsp;double</CODE></TD>
<TD><CODE><A HREF="../../../cern/jet/math/Bessel.html#k0e(double)">k0e</A>(double&nbsp;x)</CODE>

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Returns the exponentially scaled modified Bessel function
 of the third kind of order 0 of the argument.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%">
<CODE>static&nbsp;double</CODE></TD>
<TD><CODE><A HREF="../../../cern/jet/math/Bessel.html#k1(double)">k1</A>(double&nbsp;x)</CODE>

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Returns the modified Bessel function of the third kind
 of order 1 of the argument.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%">
<CODE>static&nbsp;double</CODE></TD>
<TD><CODE><A HREF="../../../cern/jet/math/Bessel.html#k1e(double)">k1e</A>(double&nbsp;x)</CODE>

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Returns the exponentially scaled modified Bessel function
 of the third kind of order 1 of the argument.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%">
<CODE>static&nbsp;double</CODE></TD>
<TD><CODE><A HREF="../../../cern/jet/math/Bessel.html#kn(int, double)">kn</A>(int&nbsp;nn,
 double&nbsp;x)</CODE>

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Returns the modified Bessel function of the third kind
 of order <tt>nn</tt> of the argument.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%">
<CODE>static&nbsp;double</CODE></TD>
<TD><CODE><A HREF="../../../cern/jet/math/Bessel.html#y0(double)">y0</A>(double&nbsp;x)</CODE>

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Returns the Bessel function of the second kind of order 0 of the argument.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%">
<CODE>static&nbsp;double</CODE></TD>
<TD><CODE><A HREF="../../../cern/jet/math/Bessel.html#y1(double)">y1</A>(double&nbsp;x)</CODE>

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Returns the Bessel function of the second kind of order 1 of the argument.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%">
<CODE>static&nbsp;double</CODE></TD>
<TD><CODE><A HREF="../../../cern/jet/math/Bessel.html#yn(int, double)">yn</A>(int&nbsp;n,
 double&nbsp;x)</CODE>

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Returns the Bessel function of the second kind of order <tt>n</tt> of the argument.</TD>
</TR>
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Method Detail</TD>
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</TABLE>

<A NAME="i0(double)"></A><H3>
i0</H3>
<PRE>
public static double i0(double&nbsp;x)
 throws <A HREF="http://java.sun.com/j2se/1.4/docs/api/java/lang/ArithmeticException.html" title="class or interface in java.lang">ArithmeticException</A></PRE>
<DL>
<DD>Returns the modified Bessel function of order 0 of the
 argument.
 
 The function is defined as <tt>i0(x) = j0( ix )</tt>.
 
 The range is partitioned into the two intervals [0,8] and
 (8, infinity). Chebyshev polynomial expansions are employed
 in each interval.

<DD><DL>
<DT>Parameters:<DD><CODE>x</CODE> - the value to compute the bessel function of.
<DT>Throws:
<DD><CODE><A HREF="http://java.sun.com/j2se/1.4/docs/api/java/lang/ArithmeticException.html" title="class or interface in java.lang">ArithmeticException</A></CODE></DL>
</DD>
</DL>
<HR>

<A NAME="i0e(double)"></A><H3>
i0e</H3>
<PRE>
public static double i0e(double&nbsp;x)
 throws <A HREF="http://java.sun.com/j2se/1.4/docs/api/java/lang/ArithmeticException.html" title="class or interface in java.lang">ArithmeticException</A></PRE>
<DL>
<DD>Returns the exponentially scaled modified Bessel function
 of order 0 of the argument.
 
 The function is defined as <tt>i0e(x) = exp(-|x|) j0( ix )</tt>.

<DD><DL>
<DT>Parameters:<DD><CODE>x</CODE> - the value to compute the bessel function of.
<DT>Throws:
<DD><CODE><A HREF="http://java.sun.com/j2se/1.4/docs/api/java/lang/ArithmeticException.html" title="class or interface in java.lang">ArithmeticException</A></CODE></DL>
</DD>
</DL>
<HR>

<A NAME="i1(double)"></A><H3>
i1</H3>
<PRE>
public static double i1(double&nbsp;x)
 throws <A HREF="http://java.sun.com/j2se/1.4/docs/api/java/lang/ArithmeticException.html" title="class or interface in java.lang">ArithmeticException</A></PRE>
<DL>
<DD>Returns the modified Bessel function of order 1 of the
 argument.
 
 The function is defined as <tt>i1(x) = -i j1( ix )</tt>.
 
 The range is partitioned into the two intervals [0,8] and
 (8, infinity). Chebyshev polynomial expansions are employed
 in each interval.

<DD><DL>
<DT>Parameters:<DD><CODE>x</CODE> - the value to compute the bessel function of.
<DT>Throws:
<DD><CODE><A HREF="http://java.sun.com/j2se/1.4/docs/api/java/lang/ArithmeticException.html" title="class or interface in java.lang">ArithmeticException</A></CODE></DL>
</DD>
</DL>
<HR>

<A NAME="i1e(double)"></A><H3>
i1e</H3>
<PRE>
public static double i1e(double&nbsp;x)
 throws <A HREF="http://java.sun.com/j2se/1.4/docs/api/java/lang/ArithmeticException.html" title="class or interface in java.lang">ArithmeticException</A></PRE>
<DL>
<DD>Returns the exponentially scaled modified Bessel function
 of order 1 of the argument.
 
 The function is defined as <tt>i1(x) = -i exp(-|x|) j1( ix )</tt>.

<DD><DL>
<DT>Parameters:<DD><CODE>x</CODE> - the value to compute the bessel function of.
<DT>Throws:
<DD><CODE><A HREF="http://java.sun.com/j2se/1.4/docs/api/java/lang/ArithmeticException.html" title="class or interface in java.lang">ArithmeticException</A></CODE></DL>
</DD>
</DL>
<HR>

<A NAME="j0(double)"></A><H3>
j0</H3>
<PRE>
public static double j0(double&nbsp;x)
 throws <A HREF="http://java.sun.com/j2se/1.4/docs/api/java/lang/ArithmeticException.html" title="class or interface in java.lang">ArithmeticException</A></PRE>
<DL>
<DD>Returns the Bessel function of the first kind of order 0 of the argument.

<DD><DL>
<DT>Parameters:<DD><CODE>x</CODE> - the value to compute the bessel function of.
<DT>Throws:
<DD><CODE><A HREF="http://java.sun.com/j2se/1.4/docs/api/java/lang/ArithmeticException.html" title="class or interface in java.lang">ArithmeticException</A></CODE></DL>
</DD>
</DL>
<HR>

<A NAME="j1(double)"></A><H3>
j1</H3>
<PRE>
public static double j1(double&nbsp;x)
 throws <A HREF="http://java.sun.com/j2se/1.4/docs/api/java/lang/ArithmeticException.html" title="class or interface in java.lang">ArithmeticException</A></PRE>
<DL>
<DD>Returns the Bessel function of the first kind of order 1 of the argument.

<DD><DL>
<DT>Parameters:<DD><CODE>x</CODE> - the value to compute the bessel function of.
<DT>Throws:
<DD><CODE><A HREF="http://java.sun.com/j2se/1.4/docs/api/java/lang/ArithmeticException.html" title="class or interface in java.lang">ArithmeticException</A></CODE></DL>
</DD>
</DL>
<HR>

<A NAME="jn(int, double)"></A><H3>
jn</H3>
<PRE>
public static double jn(int&nbsp;n,
 double&nbsp;x)
 throws <A HREF="http://java.sun.com/j2se/1.4/docs/api/java/lang/ArithmeticException.html" title="class or interface in java.lang">ArithmeticException</A></PRE>
<DL>
<DD>Returns the Bessel function of the first kind of order <tt>n</tt> of the argument.

<DD><DL>
<DT>Parameters:<DD><CODE>n</CODE> - the order of the Bessel function.<DD><CODE>x</CODE> - the value to compute the bessel function of.
<DT>Throws:
<DD><CODE><A HREF="http://java.sun.com/j2se/1.4/docs/api/java/lang/ArithmeticException.html" title="class or interface in java.lang">ArithmeticException</A></CODE></DL>
</DD>
</DL>
<HR>

<A NAME="k0(double)"></A><H3>
k0</H3>
<PRE>
public static double k0(double&nbsp;x)
 throws <A HREF="http://java.sun.com/j2se/1.4/docs/api/java/lang/ArithmeticException.html" title="class or interface in java.lang">ArithmeticException</A></PRE>
<DL>
<DD>Returns the modified Bessel function of the third kind
 of order 0 of the argument.
 
 The range is partitioned into the two intervals [0,8] and
 (8, infinity). Chebyshev polynomial expansions are employed
 in each interval.

<DD><DL>
<DT>Parameters:<DD><CODE>x</CODE> - the value to compute the bessel function of.
<DT>Throws:
<DD><CODE><A HREF="http://java.sun.com/j2se/1.4/docs/api/java/lang/ArithmeticException.html" title="class or interface in java.lang">ArithmeticException</A></CODE></DL>
</DD>
</DL>
<HR>

<A NAME="k0e(double)"></A><H3>
k0e</H3>
<PRE>
public static double k0e(double&nbsp;x)
 throws <A HREF="http://java.sun.com/j2se/1.4/docs/api/java/lang/ArithmeticException.html" title="class or interface in java.lang">ArithmeticException</A></PRE>
<DL>
<DD>Returns the exponentially scaled modified Bessel function
 of the third kind of order 0 of the argument.

<DD><DL>
<DT>Parameters:<DD><CODE>x</CODE> - the value to compute the bessel function of.
<DT>Throws:
<DD><CODE><A HREF="http://java.sun.com/j2se/1.4/docs/api/java/lang/ArithmeticException.html" title="class or interface in java.lang">ArithmeticException</A></CODE></DL>
</DD>
</DL>
<HR>

<A NAME="k1(double)"></A><H3>
k1</H3>
<PRE>
public static double k1(double&nbsp;x)
 throws <A HREF="http://java.sun.com/j2se/1.4/docs/api/java/lang/ArithmeticException.html" title="class or interface in java.lang">ArithmeticException</A></PRE>
<DL>
<DD>Returns the modified Bessel function of the third kind
 of order 1 of the argument.
 
 The range is partitioned into the two intervals [0,2] and
 (2, infinity). Chebyshev polynomial expansions are employed
 in each interval.

<DD><DL>
<DT>Parameters:<DD><CODE>x</CODE> - the value to compute the bessel function of.
<DT>Throws:
<DD><CODE><A HREF="http://java.sun.com/j2se/1.4/docs/api/java/lang/ArithmeticException.html" title="class or interface in java.lang">ArithmeticException</A></CODE></DL>
</DD>
</DL>
<HR>

<A NAME="k1e(double)"></A><H3>
k1e</H3>
<PRE>
public static double k1e(double&nbsp;x)
 throws <A HREF="http://java.sun.com/j2se/1.4/docs/api/java/lang/ArithmeticException.html" title="class or interface in java.lang">ArithmeticException</A></PRE>
<DL>
<DD>Returns the exponentially scaled modified Bessel function
 of the third kind of order 1 of the argument.
 
 <tt>k1e(x) = exp(x) * k1(x)</tt>.

<DD><DL>
<DT>Parameters:<DD><CODE>x</CODE> - the value to compute the bessel function of.
<DT>Throws:
<DD><CODE><A HREF="http://java.sun.com/j2se/1.4/docs/api/java/lang/ArithmeticException.html" title="class or interface in java.lang">ArithmeticException</A></CODE></DL>
</DD>
</DL>
<HR>

<A NAME="kn(int, double)"></A><H3>
kn</H3>
<PRE>
public static double kn(int&nbsp;nn,
 double&nbsp;x)
 throws <A HREF="http://java.sun.com/j2se/1.4/docs/api/java/lang/ArithmeticException.html" title="class or interface in java.lang">ArithmeticException</A></PRE>
<DL>
<DD>Returns the modified Bessel function of the third kind
 of order <tt>nn</tt> of the argument.
 
 The range is partitioned into the two intervals [0,9.55] and
 (9.55, infinity). An ascending power series is used in the
 low range, and an asymptotic expansion in the high range.

<DD><DL>
<DT>Parameters:<DD><CODE>nn</CODE> - the order of the Bessel function.<DD><CODE>x</CODE> - the value to compute the bessel function of.
<DT>Throws:
<DD><CODE><A HREF="http://java.sun.com/j2se/1.4/docs/api/java/lang/ArithmeticException.html" title="class or interface in java.lang">ArithmeticException</A></CODE></DL>
</DD>
</DL>
<HR>

<A NAME="y0(double)"></A><H3>
y0</H3>
<PRE>
public static double y0(double&nbsp;x)
 throws <A HREF="http://java.sun.com/j2se/1.4/docs/api/java/lang/ArithmeticException.html" title="class or interface in java.lang">ArithmeticException</A></PRE>
<DL>
<DD>Returns the Bessel function of the second kind of order 0 of the argument.

<DD><DL>
<DT>Parameters:<DD><CODE>x</CODE> - the value to compute the bessel function of.
<DT>Throws:
<DD><CODE><A HREF="http://java.sun.com/j2se/1.4/docs/api/java/lang/ArithmeticException.html" title="class or interface in java.lang">ArithmeticException</A></CODE></DL>
</DD>
</DL>
<HR>

<A NAME="y1(double)"></A><H3>
y1</H3>
<PRE>
public static double y1(double&nbsp;x)
 throws <A HREF="http://java.sun.com/j2se/1.4/docs/api/java/lang/ArithmeticException.html" title="class or interface in java.lang">ArithmeticException</A></PRE>
<DL>
<DD>Returns the Bessel function of the second kind of order 1 of the argument.

<DD><DL>
<DT>Parameters:<DD><CODE>x</CODE> - the value to compute the bessel function of.
<DT>Throws:
<DD><CODE><A HREF="http://java.sun.com/j2se/1.4/docs/api/java/lang/ArithmeticException.html" title="class or interface in java.lang">ArithmeticException</A></CODE></DL>
</DD>
</DL>
<HR>

<A NAME="yn(int, double)"></A><H3>
yn</H3>
<PRE>
public static double yn(int&nbsp;n,
 double&nbsp;x)
 throws <A HREF="http://java.sun.com/j2se/1.4/docs/api/java/lang/ArithmeticException.html" title="class or interface in java.lang">ArithmeticException</A></PRE>
<DL>
<DD>Returns the Bessel function of the second kind of order <tt>n</tt> of the argument.

<DD><DL>
<DT>Parameters:<DD><CODE>n</CODE> - the order of the Bessel function.<DD><CODE>x</CODE> - the value to compute the bessel function of.
<DT>Throws:
<DD><CODE><A HREF="http://java.sun.com/j2se/1.4/docs/api/java/lang/ArithmeticException.html" title="class or interface in java.lang">ArithmeticException</A></CODE></DL>
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Rabbit simulation

initial commit