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<html>
<head>
<title>
CHEBYSHEV_SERIES - Evaluate Chebyshev Series with Derivatives
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
CHEBYSHEV_SERIES <br> Evaluate Chebyshev Series with Derivatives
</h1>
<hr>
<p>
<b>CHEBYSHEV_SERIES</b>
is a C++ library which
can evaluate a Chebyshev series approximating a function f(x),
while efficiently computing one, two or three derivatives of the
series, which approximate f'(x), f''(x), and f'''(x),
by Manfred Zimmer.
</p>
<p>
Note that this library does not compute a Chebyshev series;
it assumes that the series has already been computed, and
offers an efficient means of evaluating the series and its derivatives
simultaneously.
</p>
<h3 align = "center">
Licensing:
</h3>
<p>
The computer code and data files made available on this
web page are distributed under
<a href = "../../txt/gnu_lgpl.txt">the GNU LGPL license.</a>
</p>
<h3 align = "center">
Languages:
</h3>
<p>
<b>CHEBYSHEV_SERIES</b> is available in
<a href = "../../c_src/chebyshev_series/chebyshev_series.html">a C version</a> and
<a href = "../../cpp_src/chebyshev_series/chebyshev_series.html">a C++ version</a> and
<a href = "../../f77_src/chebyshev_series/chebyshev_series.html">a FORTRAN77 version</a> and
<a href = "../../f_src/chebyshev_series/chebyshev_series.html">a FORTRAN90 version</a> and
<a href = "../../m_src/chebyshev_series/chebyshev_series.html">a MATLAB version</a>.
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../cpp_src/chebyshev/chebyshev.html">
CHEBYSHEV</a>,
a C++ library which
computes the Chebyshev interpolant/approximant to a given function
over an interval.
</p>
<p>
<a href = "../../cpp_src/chebyshev_interp_1d/chebyshev_interp_1d.html">
CHEBYSHEV_INTERP_1D</a>,
a C++ library which
determines the combination of Chebyshev polynomials which
interpolates a set of data, so that p(x(i)) = y(i).
</p>
<p>
<a href = "../../cpp_src/chebyshev_polynomial/chebyshev_polynomial.html">
CHEBYSHEV_POLYNOMIAL</a>,
a C++ library which
considers the Chebyshev polynomials T(i,x), U(i,x), V(i,x) and W(i,x).
Functions are provided to evaluate the polynomials, determine their zeros,
produce their polynomial coefficients, produce related quadrature rules,
project other functions onto these polynomial bases, and integrate
double and triple products of the polynomials.
</p>
<p>
<a href = "../../cpp_src/fn/fn.html">
FN</a>,
a C++ library which
approximates elementary and special functions using Chebyshev polynomials;
functions include Airy, Bessel I, J, K and Y, beta,
confluent hypergeometric, error, gamma, log gamma, Pochhammer, Spence;
integrals include hyperbolic cosine, cosine, Dawson, exponential,
logarithmic, hyperbolic sine, sine; by Wayne Fullerton.
</p>
<p>
<a href = "../../cpp_src/polpak/polpak.html">
POLPAK</a>,
a C++ library which
evaluates a variety of mathematical functions, including
Chebyshev, Gegenbauer, Hermite, Jacobi, Laguerre, Legendre polynomials,
and the Collatz sequence.
</p>
<p>
<a href = "../../cpp_src/toms446/toms446.html">
TOMS446</a>,
a C++ library which
manipulates Chebyshev series for interpolation and approximation;
this is ACM TOMS algorithm 446,
by Roger Broucke.
</p>
<h3 align = "center">
Author:
</h3>
<p>
Manfred Zimmer
</p>
<h3 align = "center">
Reference:
</h3>
<p>
<ol>
<li>
Charles Clenshaw,<br>
Mathematical Tables, Volume 5,<br>
Chebyshev series for mathematical functions,<br>
London, 1962.
</li>
<li>
Gerhard Maess,<br>
Vorlesungen ueber Numerische Mathematik II, Analysis,<br>
Berlin, Akademie_Verlag, 1984-1988,<br>
ISBN: 978-3764318840,<br>
LC: QA297.M325.
</li>
<li>
Francis Smith,<br>
An algorithm for summing orthogonal polynomial series and their
derivatives with applications to curve-fitting and interpolation,<br>
Mathematics of Computation,<br>
Volume 19, Number 89, 1965, pages 33-36.
</li>
</ol>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "chebyshev_series.cpp">chebyshev_series.cpp</a>, the source code.
</li>
<li>
<a href = "chebyshev_series.hpp">chebyshev_series.hpp</a>, the include file.
</li>
<li>
<a href = "chebyshev_series.sh">chebyshev_series.sh</a>,
BASH commands to compile the source code.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<ul>
<li>
<a href = "chebyshev_series_prb.cpp">chebyshev_series_prb.cpp</a>,
a sample calling program.
</li>
<li>
<a href = "chebyshev_series_prb.sh">chebyshev_series_prb.sh</a>,
BASH commands to compile and run the sample program.
</li>
<li>
<a href = "chebyshev_series_prb_output.txt">chebyshev_series_prb_output.txt</a>,
the output file.
</li>
</ul>
</p>
<h3 align = "center">
List of Routines:
</h3>
<p>
<ul>
<li>
<b>ECHEBSER0</b> evaluates a Chebyshev series.
</li>
<li>
<b>ECHEBSER1</b> evaluates a Chebyshev series and first derivative.
</li>
<li>
<b>ECHEBSER2</b> evaluates a Chebyshev series and two derivatives.
</li>
<li>
<b>ECHEBSER3</b> evaluates a Chebyshev series and three derivatives.
</li>
<li>
<b>ECHEBSER4</b> evaluates a Chebyshev series and four derivatives.
</li>
<li>
<b>EVENCHEBSER0</b> evaluates an even Chebyshev series.
</li>
<li>
<b>EVENCHEBSER1</b> evaluates an even Chebyshev series and first derivative.
</li>
<li>
<b>EVENCHEBSER2</b> evaluates an even Chebyshev series and first two derivatives.
</li>
<li>
<b>ODDCHEBSER0</b> evaluates an odd Chebyshev series.
</li>
<li>
<b>ODDCHEBSER1</b> evaluates an odd Chebyshev series and the first derivative.
</li>
<li>
<b>ODDCHEBSER2</b> evaluates an odd Chebyshev series and first two derivatives.
</li>
<li>
<b>TIMESTAMP</b> prints the current YMDHMS date as a time stamp.
</li>
</ul>
</p>
<p>
You can go up one level to <a href = "../cpp_src.html">
the C++ source codes</a>.
</p>
<hr>
<i>
Last revised on 29 April 2014.
</i>
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