CLAUSEN
Chebyshev Interpolant to the Clausen Function

CLAUSEN is a C++ library which evaluates a Chebyshev interpolant to the Clausen function Cl2(x).

Cl2(x) = - integral ( 0 < s < x ) log ( abs ( 2 sin ( x / 2 ) ) ) dx

The Clausen function is periodic, with period 2 pi.

Licensing:

The computer code and data files made available on this web page are distributed under the GNU LGPL license.

Languages:

CLAUSEN is available in a C version and a C++ version and a FORTRAN90 version and a MATLAB version and a Python version.

Related Data and Programs:

CHEBYSHEV, a C++ library which computes the Chebyshev interpolant/approximant to a given function over an interval.

CHEBYSHEV_INTERP_1D, a C++ library which determines the combination of Chebyshev polynomials which interpolates a set of data, so that p(x(i)) = y(i).

CHEBYSHEV_POLYNOMIAL, 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.

CHEBYSHEV_SERIES, 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.

FN, 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.

POLPAK, a C++ library which evaluates a variety of mathematical functions, including Chebyshev, Gegenbauer, Hermite, Jacobi, Laguerre, Legendre polynomials, and the Collatz sequence.

TEST_VALUES, a C++ library which supplies test values of various mathematical functions.

TOMS446, a C++ library which manipulates Chebyshev series for interpolation and approximation; this is ACM TOMS algorithm 446, by Roger Broucke.

Reference:

1. Kurt Koelbig,
   Chebyshev coefficients for the Clausen function Cl2(x),
   Journal of Computational and Applied Mathematics,
   Volume 64, Number 3, 1995, pages 295-297.

Source Code:

• clausen.cpp, the source code.
• clausen.hpp, the include file.

Examples and Tests:

• clausen_test.cpp, a sample calling program.
• clausen_test.txt, the output file.

List of Routines:

• CLAUSEN evaluates the Clausen function Cl2(x).
• CLAUSEN_VALUES returns some values of the Clausen's integral.
• R8_CSEVL evaluates a Chebyshev series.
• R8_WRAP forces an R8 to lie between given limits by wrapping.
• TIMESTAMP prints the current YMDHMS date as a time stamp.

You can go up one level to the C++ source codes.