Communications of the
Korean Mathematical Society CKMS

Since the time of Euler, the dilogarithm and polylogarithm functions have been studied by many mathematicians who used various notations for the dilogarithm function ${\text {Li}}_2(z)$. These functions are related to many other mathematical functions and have a variety of application. The main objective of this paper is to present corrected versions of two equivalent factorization formulas involving the Legendre's Chi-function $\chi_2$ and an evaluation of a class of integrals which is useful to evaluate some integrals associated with the dilogarithm function.

Keywords: dilogarithm function, polylogarithm function, Legendre's chi-function, gamma function, Riemann Zeta function, Euler-Mascheroni's constant

MSC numbers: Primary 33E20; Secondary 11M41