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<HTML>
<HEAD>
<TITLE>Chebyshev polynomial</TITLE>
</HEAD>
<BODY bgcolor="#FFFFFF" fgcolor="#000000">
<P>
<font size="+3" color="green"><B>Chebyshev polynomial</B></font></P>
<P>
<TABLE border="1" cols="2" frame="box" rules="all" width="572">
<TR>
<TD width="15%" valign="top"><B>Syntax</B>:</TD>
<TD width="85%"><CODE>
y = CHEBY(n,x)</code>
</TD></TR>
</table></p>
<p>
In the Sturm-Liouville boundary value problem, there is a special case, called
Chebyshev's differential equation, which is defined as:</p>
<p>
<img src="cheby1.png"></p>
<p>
where <i>n</i> is a real number. The solutions of this equation are called
Chebyshev functions of degree <i>n</i>.</p>
<p>
If <i>n</i> is a non-negative integer, the Chebyshev functions are often referred
to as Chebyshev polynomials, <img align="top" src="cheby2.png"></p>
<p>
The Chebyshev polynomials can be expressed by Rodrigues' formula:</p>
<p>
<IMG SRC="cheby3.png"></P>
<p>
or by</p>
<p>
<img SRC="cheby4.png"></p>
<P>
<a href="../Beta/beta.htm"><img align="top" border="0" src="../../../shadow_left.gif">
<font size="+1" color="olive">Beta functions</font></a><br />
<a href="../Convolute/convolute.htm"><img align="top" border="0" src="../../../shadow_right.gif">
<font size="+1" color="olive">Convolute function</font></a>
</P>
</BODY>
</HTML>
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