Clausen's Integral

$\begin{figure}\begin{center}\BoxedEPSF{ClausensIntegral.epsf}\end{center}\end{figure}$

The Clausen Function

$\begin{displaymath} \mathop{\it Cl}\nolimits _2(\theta)=-\int_0^\theta \ln[2\sin({\textstyle{1\over 2}}t)]\,dt. \end{displaymath}$

See also Clausen Function

References

Abramowitz, M. and Stegun, C. A. (Eds.). Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing. New York: Dover, pp. 1005-1006, 1972.

Ashour, A. and Sabri, A. ``Tabulation of the Function $\psi(\theta)=\sum_{n=1}^\infty {\sin(n\theta)\over n^2}$ .'' Math. Tables Aids Comp. 10, 54 and 57-65, 1956.

Clausen, R. ``Über die Zerlegung reeller gebrochener Funktionen.'' J. reine angew. Math. 8, 298-300, 1832.