2 problems

Let $\chi(\kappa,k_F,L)$ be the generating function with Fisher–Hartwig expansion … whose two parts are given by equations (1) and (2). The parameter $\kappa$ may have half-integer…

Let $F_1(k_F,\lambda)$ denote the coefficient of $L^{-1}$ in the expansion … for the full-counting-statistics generating function of one-dimensional free fermions. The cubic coeffi…