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<table width="100%" summary="page for chebyshev.s.quadrature.rules"><tr><td>chebyshev.s.quadrature.rules</td><td style="text-align: right;">R Documentation</td></tr></table>

<h2> Create list of Chebyshev quadrature rules </h2>

<h3>Description</h3>

<p>This function returns a list with <i>n</i> elements containing 
the order <i>k</i> quadrature rule data frame for 
the Chebyshev S polynomial
for orders <i>k = 1,\;2,\; &hellip; ,\;n</i>.
</p>


<h3>Usage</h3>

<pre>
chebyshev.s.quadrature.rules(n,normalized=FALSE)
</pre>


<h3>Arguments</h3>

<table summary="R argblock">
<tr valign="top"><td><code>n</code></td>
<td>
<p> integer value for the highest order </p>
</td></tr>
<tr valign="top"><td><code>normalized</code></td>
<td>
<p> boolean value.  if TRUE rules are for orthonormal
polynomials, otherwise they are for orthgonal polynomials </p>
</td></tr>
</table>


<h3>Details</h3>

<p>An order <i>k</i> quadrature data frame is a named data frame that contains 
the roots and abscissa values of the corresponding order <i>k</i> orthogonal polynomial.  
The column with name <code>x</code> contains the roots or zeros and 
the column with name <code>w</code> contains the weights.
</p>


<h3>Value</h3>

<p>A list with <i>n</i> elements each of which is a data frame
</p>
<table summary="R valueblock">
<tr valign="top"><td><code>1 </code></td>
<td>
<p>Quadrature rule data frame for the order 1 Chebyshev polynomial</p>
</td></tr>
<tr valign="top"><td><code>2 </code></td>
<td>
<p>Quadrature rule data frame for the order 2 Chebyshev polynomial</p>
</td></tr>
</table>
<p>...
</p>
<table summary="R valueblock">
<tr valign="top"><td><code>n </code></td>
<td>
<p>Quadrature rule data frame for the order <i>n</i> Chebyshev polynomial</p>
</td></tr>
</table>


<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>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>Stroud, A. H., and D. Secrest, 1966. <em>Gaussian Quadrature Formulas</em>,
Prentice-Hall, Englewood Cliffs, NJ.
</p>


<h3>See Also</h3>

<p><code>quadrature.rules</code>,
<code>chebyshev.s.quadrature</code>
</p>


<h3>Examples</h3>

<pre>
###
### generate a list of quadrature rules for
### the Chebyshev S orthogonal polynomials
### for orders 1 to 5
###
orthogonal.rules &lt;- chebyshev.s.quadrature.rules( 5 )
print( orthogonal.rules )
###
### generate a list of quadrature rules for
### the Chebyshev S orthogonal polynomials
### for orders 1 to 5
###
orthonormal.rules &lt;- chebyshev.s.quadrature.rules( 5, TRUE )
print( orthonormal.rules )
</pre>


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