Fermionic Basis in Conformal Field Theory and Thermodynamic Bethe Ansatz for Excited States II

We consider the XXZ spin chain in the scaling limit in the Matsubara direction. The main result of this paper is new representations for the functions $\mathrm{\Psi }(l,\kappa )$ and $\mathrm{\Theta }(l,m;\kappa ,\alpha )$ associated with the function $\omega (\zeta ,\xi ;\kappa ,\kappa )$ found in the expression for the correlation function of the generators of the fermionic basis for the XXZ spin chain. The final result incorporates the case of particle-hole excitations which is needed for the relation of the fermionic basis to the Virasoro basis of the CFT descendants.