  In this paper, we will consider the free probability theory of free group
factor $L(F_{N}),$ where $F_{k}$ is the free group with $k$-generators. We
compute the moment series and the R-transform of the generating operator,
$T=g_{1}+...+g_{N}+g_{1}^{-1}+..+g_{N}^{-1}.$
