C326: Clausen Function

Author(s): K.S. Kölbig	Library: MATHLIB
Submitter:	Submitted: 01.12.1994
Language: Fortran	Revised:

Function subprograms RCLAUS and DCLAUS calculate the Clausen function

for real arguments x.

On CDC and Cray computers, the double-precision version DCLAUS is not available.

Structure:

FUNCTION subprograms
User Entry Names: RCLAUS, DCLAUS

Usage:

In any arithmetic expression,

RCLAUS(X) or DCLAUS(X) has the value ,

where RCLAUS is of type REAL, DCLAUS is of type DOUBLE PRECISION, and X has the same type as the function name.

Method:

For , the function is approximated by truncated Chebyshev series. For x outside this range, the relations and are used.

Accuracy:

RCLAUS (except on CDC and Cray computers) has full single-precision accuracy in the interval . For most values of the argument , DCLAUS (and RCLAUS on CDC and Cray computers) has an accuracy of approximately one significant digit less than the machine precision. Accuracy is lost near the zero of at and for large values of |x|.

References:

1. K.S. Kölbig, Chebyshev coefficients for the Clausen function , J. Comput. Appl. Math. 64 (1995) 295-297.