C332 Dilogarithm Function

Function subprograms RDILOG and DDILOG calculate the dilogarithm function

$Li$₂(x) = -∫₀^x{ln|1-t|t}dt

for real arguments x.

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

Structure:

FUNCTION subprograms
User Entry Names: RDILOG, DDILOG
Obsolete User Entry Names: DILOG $\equiv$ RDILOG

Usage:

In any arithmetic expression, RDILOG(X) or DDILOG(X) has the value $Li$₂(X) ,

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

Method:

Approximation by truncated Chebyshev series and functional relations.

Accuracy:

RDILOG (except on CDC and Cray computers) has full single-precision accuracy. For most values of the argument X, DDILOG (and RDILOG on CDC and Cray computers) has an accuracy of approximately one significant digit less than the machine precision.

References:

1. Y.L. Luke, Mathematical functions and their approximations, (Academic Press, New York 1975) 67.

C334