at least $16$ digits precision at $T=0.9$ and $8$ digits at $T=0.5$, and for the ground state energy $E_{0}=-.76321\pm .00003$ in agreement with Parisi’s estimate $E_{0}=-.7633\pm .0001$ [@P80]. A similar analysis can be used to determine the value of $x_{\rm max}$ as a function of temperature, the result is shown in Fig. \[fig:xmaxpad\]. The value of the breaking point is finite in the limit $T\rightarrow 0$ $$\label{xmax}
x_{max}(0)=.548\pm .005,$$ see inset Figure \[fig:xmaxpad\], and slightly larger than the value $1/2$ predicted by the Parisi-Toulouse scaling, in agreement with the approximate nature of this relation [@VTP81; @PT80].

The analysis of the function $q(x,T)$ is more complex, because not only the Taylor expansion of $q(x)$ in powers of $x$ around any $0<x<x_{max}$ is likely to be asymptotic for any fixed temperature, but the expansion in $\tau$ of the coefficients of the $x$-expansion are themselves non convergent. Therefore one should use a double Padè expansion, one for the coefficients and one for $q(x)$. The procedure however is quite difficult because we do not have a systematic way of choosing the best approximant and, moreover, coefficients of higher order are known with less precision in $\tau$. A better approach is to construct the function 