CLAUSEN
Chebyshev Interpolant to the Clausen Function

CLAUSEN is a Python 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_POLYNOMIAL, a Python 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.

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

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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.py, evaluates the Clausen function using a Chebyshev series.
• clausen_test.sh, a sample calling program.
• clausen_test.txt, the output file.

You can go up one level to the Python source codes.