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<table width="100%" summary="page for chebyshev.s.weight"><tr><td>chebyshev.s.weight</td><td style="text-align: right;">R Documentation</td></tr></table>

<h2> Weight function for the Chebyshev polynomial </h2>

<h3>Description</h3>

<p>This function returns the value of the weight function for the order <i>k</i> Chebyshev polynomial of the second kind, <i>S_k &le;ft( x \right) </i>.
</p>


<h3>Usage</h3>

<pre>
chebyshev.s.weight(x)
</pre>


<h3>Arguments</h3>

<table summary="R argblock">
<tr valign="top"><td><code>x</code></td>
<td>
<p> the function argument which can be a vector </p>
</td></tr>
</table>


<h3>Details</h3>

<p>The function takes on non-zero values in the interval <i> &le;ft( -2,2 \right) </i>.  The formula
used to compute the weight function is as follows.
</p>
<p><i>w&le;ft( x \right) = &radic; {1 - \frac{{x^2 }}{4}}</i>
</p>


<h3>Value</h3>

<p>The value of the weight function.
</p>


<h3>Author(s)</h3>

<p> Frederick Novomestky <a href="mailto:fnovomes@poly.edu">fnovomes@poly.edu</a> </p>


<h3>References</h3>

<p>Abramowitz, M. and I. A. Stegun, 1968. <em>Handbook of Mathematical Functions with
Formulas, Graphs, and Mathematical Tables</em>, Dover Publications, Inc., New York.
</p>
<p>Courant, R., and D. Hilbert, 1989. <em>Methods of Mathematical Physics</em>,
John Wiley, New York, NY.
</p>
<p>Press, W. H., S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, 1992. 
<em>Numerical Recipes in C</em>, Cambridge University Press, Cambridge, U.K.
</p>
<p>Szego, G., 1939. <em>Orthogonal Polynomials</em>, 23, American Mathematical Society
Colloquium Publications, Providence, RI.
</p>


<h3>Examples</h3>

<pre>
###
### compute the S Chebyshev weight function for arguments between -2 and 2
###
x &lt;- seq( -2, 2, .01 )
y &lt;- chebyshev.s.weight( x )
plot( x, y )
</pre>


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