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<table width="100%" summary="page for chebyshev.s.recurrences"><tr><td>chebyshev.s.recurrences</td><td style="text-align: right;">R Documentation</td></tr></table>

<h2> Recurrence relations for Chebyshev polynomials </h2>

<h3>Description</h3>

<p>This function returns a data frame with <i>n + 1</i> rows and four named columns containing 
the coefficient vectors <b>c</b>, <b>d</b>, <b>e</b> and <b>f</b> of 
the recurrence relations for the order <i>k</i> Chebyshev polynomial of the second kind, <i>S_k &le;ft( x \right)</i>, 
and for orders <i>k = 0,\;1,\; &hellip; ,\;n</i>.
</p>


<h3>Usage</h3>

<pre>
chebyshev.s.recurrences(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> boolean value which, if TRUE, returns recurrence relations for normalized polynomials </p>
</td></tr>
</table>


<h3>Value</h3>

<p>A data frame with the recurrence relation parameters.
</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>Szego, G., 1939. <em>Orthogonal Polynomials</em>, 23, American Mathematical Society
Colloquium Publications, Providence, RI.
</p>


<h3>See Also</h3>

<p><code>chebyshev.s.inner.products</code>
</p>


<h3>Examples</h3>

<pre>
###
### generate the recurrences data frame for 
### the normalized Chebyshev S polynomials
### of orders 0 to 10.
###
normalized.r &lt;- chebyshev.s.recurrences( 10, normalized=TRUE )
print( normalized.r )
###
### generate the recurrences data frame for 
### the normalized Chebyshev S polynomials
### of orders 0 to 10.
###
unnormalized.r &lt;- chebyshev.s.recurrences( 10, normalized=FALSE )
print( unnormalized.r )
</pre>


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