Log-Sine integrals involving series associated with the zeta function and polylogarithms

Abstract

Motivated essentially by their potential for applications in a wide range of mathematical and physical problems, the Log-Sine integrals have been evaluated, in the existing literature on the subject, in many different ways. The main object of this paper is to show how nicely some general formulas analogous to the generalized Log-Sine integral $Ls_n^{(m)}\left(\frac{\pi}{3}\right)$ can be obtained by using the theory of Polylogarithms. Relevant connections of the results presented here with those obtained in earlier works are also indicated precisely.