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We consider the XXZ spin chain in the scaling limit in the Matsubaradirection. The main result of this paper is new representations for thefunctions $\Psi(l, \kappa)$ and $\Theta(l, m; \kappa, \alpha)$ associated withthe function $\omega(\zeta, \xi; \kappa, \kappa)$ found in the expression forthe correlation function of the generators of the fermionic basis for the XXZspin chain. The final result incorporates the case of particle-hole excitationswhich is needed for the relation of the fermionic basis to the Virasoro basisof the CFT descendants.

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