  We present the exact solution to the moment problem for the spin-1/2
isotropic antiferromagnetic XY chain with explicit forms for the moments with
respect to the Neel state, the cumulant generating function, and the Resolvent
Operator. We verify the correctness of the Horn-Weinstein Theorems, but the
analytic structure of the generating function <e^{-tH}> in the complex t-plane
is quite different from that assumed by the "t"-Expansion and the Connected
Moments Expansion due to the vanishing gap. This function has a finite radius
of convergence about t=0, and for large t has a leading descending algebraic
series E(t)-E_0 ~ At^{-2}. The Resolvent has a branch cut and essential
singularity near the ground state energy of the form G(s)/s ~ B|s+1|^{-3/4}
exp(C|s+1|^{1/2}). Consequently extrapolation strategies based on these
assumptions are flawed and in practise we find that the CMX methods are
pathological and cannot be applied, while numerical evidence for two of the
"t"-expansion methods indicates a clear asymptotic convergence behaviour with
truncation order.
