  We study the analytic properties of the scaling function associated with the
2D Ising model free energy in the critical domain $T \to T_c$, $H \to 0$. The
analysis is based on numerical data obtained through the Truncated Free Fermion
Space Approach. We determine the discontinuities across the Yang-Lee and Langer
branch cuts. We confirm the standard analyticity assumptions and propose
"extended analyticity"; roughly speaking, the latter states that the Yang-Lee
branching point is the nearest singularity under Langer's branch cut. We
support the extended analyticity by evaluating numerically the associated
"extended dispersion relation".
