Some Identities Involving the Legendre's Chi-Function
Commun. Korean Math. Soc. 2007 Vol. 22, No. 2, 219-225
Printed June 1, 2007
Junesang Choi
Dongguk University
Abstract : 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
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