<?xml version="1.0" encoding="UTF-8"?>
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<refentry xml:id="lambdak" xml:lang="en"
          xmlns="http://docbook.org/ns/docbook"
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          xmlns:db="http://docbook.org/ns/docbook">

  <refnamediv>
    <refname>lambdak</refname><refpurpose>Evaluate lambda function for
    Affine Wigner distribution.</refpurpose>
  </refnamediv>

  <refsynopsisdiv>
    <title>Calling Sequence</title>
    <synopsis>
      Y=lambdak(U,K)
    </synopsis>
  </refsynopsisdiv>

  <refsection>
    <title>Parameters</title>
    <variablelist>
      <varlistentry>
        <term>U :</term>
        <listitem>
          <para> real vector</para>
        </listitem>
      </varlistentry>
      <varlistentry>
        <term>K :</term>
        <listitem>
          <para> real scalar</para>
        </listitem>
      </varlistentry>
      <varlistentry>
        <term>Y :</term>
        <listitem>
          <para> value of LAMBDAD at point(s) U</para>
        </listitem>
      </varlistentry>
    </variablelist>
  </refsection>

  <refsection>
    <title>Description</title>
    <para>
      lambdak evaluates the parametrization lambda function
      involved in the affine smoothed pseudo Bertrand distribution.
      <literal>lambdak(U,0) = -U/(exp(-U)-1) for K = 0</literal>
      <literal>lambdak(U,1) = exp(1+U exp(-U)/(exp(-U)-1)) for K = 1</literal>
      <literal>lambdak(U,K) = (K (exp(-U)-1)/(exp(-KU)-1))^(1/(K-1)) otherwise</literal>
    </para>
  </refsection>
  <refsection>
    <title>Examples</title>
    <programlisting role="example"><![CDATA[
    u=linspace(0.001,5,100)';
    clf;plot(u,[lambdak(u,0),lambdak(u,1),lambdak(u,2)])
    legend("k="+["0","1","2"]);
    ]]></programlisting>
    <scilab:image><![CDATA[
    u=linspace(0.001,5,100)';
    clf;plot(u,[lambdak(u,0),lambdak(u,1),lambdak(u,2)])
    legend("k="+["0","1","2"]);
    ]]></scilab:image>
  </refsection>
  <refsection>
    <title>Authors</title>
    <simplelist type="vert">
      <member>H. Nahrstaedt - Aug 2010</member>
      <member>P. Goncalves, October 95</member>
    </simplelist>
  </refsection>
</refentry>
