On the Clausen integral Cl2(Θ) and a related integral

摘要

In this article, the Clausen integral Cl2(Θ)=-∫Θ0ln(2 sin t2)dt whereby Θ is equal to a rational multiple of π belonging to ]0,2π[, is developed into a finite series of derivatives of the di-gamma function ψ. For the same values of Θ, a method is presented to calculate the related integral ∫10lnϱϱ2−2ϱcosΘ+1dϱ.