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<table width="100%" summary="page for chebyshev.s.polynomials"><tr><td>chebyshev.s.polynomials</td><td style="text-align: right;">R Documentation</td></tr></table>

<h2> Create list of Chebyshev polynomials </h2>

<h3>Description</h3>

<p>This function returns a list with <i>n + 1</i> elements containing 
the order <i>k</i> Chebyshev polynomials of the second kind, <i>S_k &le;ft( x\right)</i>, 
for orders <i>k = 0,\;1,\; &hellip; ,\;n</i>.
</p>


<h3>Usage</h3>

<pre>
chebyshev.s.polynomials(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 polynomial order </p>
</td></tr>
<tr valign="top"><td><code>normalized</code></td>
<td>
<p> a boolean value which, if TRUE, returns a list of normalized orthogonal polynomials </p>
</td></tr>
</table>


<h3>Details</h3>

<p>The function <code>chebyshev.s.recurrences</code> produces a data frame with the recurrence relation parameters
for the polynomials.  If the <code>normalized</code> argument is FALSE, the
function <code>orthogonal.polynomials</code> is used to construct the list of orthogonal polynomial objects.
Otherwise, the function <code>orthonormal.polynomials</code> is used to construct the
list of orthonormal polynomial objects.
</p>


<h3>Value</h3>

<p>A list of <i>n + 1</i> polynomial objects
</p>
<table summary="R valueblock">
<tr valign="top"><td><code>1 </code></td>
<td>
<p>order 0 Chebyshev polynomial</p>
</td></tr>
<tr valign="top"><td><code>2 </code></td>
<td>
<p>order 1 Chebyshev polynomial</p>
</td></tr>
</table>
<p>...
</p>
<table summary="R valueblock">
<tr valign="top"><td><code>n+1 </code></td>
<td>
<p>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>Courant, R., and D. Hilbert, 1989. <em>Methods of Mathematical Physics</em>,
John Wiley, New York, NY.
</p>
<p>Szego, G., 1939. <em>Orthogonal Polynomials</em>, 23, American Mathematical Society
Colloquium Publications, Providence, RI.
</p>


<h3>See Also</h3>

<p><code>chebyshev.s.recurrences</code>,
<code>orthogonal.polynomials</code>,
<code>orthonormal.polynomials</code>
</p>


<h3>Examples</h3>

<pre>
###
### gemerate a list of normalized S Chebyshev polynomials of orders 0 to 10
###
normalized.p.list &lt;- chebyshev.s.polynomials( 10, normalized=TRUE )
print( normalized.p.list )
###
### gemerate a list of unnormalized S Chebyshev polynomials of orders 0 to 10
###
unnormalized.p.list &lt;- chebyshev.s.polynomials( 10, normalized=FALSE )
print( unnormalized.p.list )
</pre>


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