with a rapidly growing number of terms we only report the limit $x\rightarrow 0$ result: $$\label{dev30}
\frac{18\dot{q}(0)}{T^{2}}+q^{(3)}(0)m'''(0,0)^{2}-\frac{38\dot{q}(0)^{2}m'''(0,0)^{2}}{T}+\dot{q}(0)^{3}m^{(0,5)}(0,0)=0$$ $$\label{eq:dev40}
q^{(4)}(0)m'''(0,0)-\frac{96\dot{q}(0)m'''(0,0)^{3}}{T}=0$$ where equation (\[limz2\]) and the exact result $ \ddot{q}(0)=0 $ have been used. Note that equation (\[eq:dev40\]), with equation (\[m30\]), gives a complete determination of the quartic derivative of $q(x)$ at $x=0$ as a function of the temperature $T$ and of the first derivative $\dot{q}(x=0)$: $$q^{(4)}(0)=-\frac{96\sqrt{2}\dot{q}(0)^{5/2}}{T^{3/2}}$$ This relation shows that the function $q(x)$ does not have a well defined parity [@Temes].

Going to higher orders one can show that all the even derivatives can be expressed in terms of the odd ones; for instance we have $$q^{(6)}(0)=-\frac{34272\sqrt{2}\dot{q}(0)^{7/2}}{T^{5/2}}
           -\frac{1056\sqrt{2}\dot{q}(0)^{3/2}q^{(3)}(0)}{T^{3/2}}$$ and so on.

In the limit $T\to 0$ we have $T\,\dot{q}(0) = 0.743\pm 0.002$. Note that if we take $\dot{q}(0)\sim 1 /T$ for $T\to 0$ the previous equations implies that all the derivatives diverge with the temperature as $q^{(n)}(0)\sim 1/T^{n}$, in agreement with the Parisi-Toulouse scaling $q(x,T)= q(\beta x)$ [@VTP81; @PT80]. Note that we have derived this scaling under strong hypothesis that it must be valid asymptotically for $T\to 0$ and $\beta x\to 0$.

This approach also provides an alternative method to compute the expansion of $q(x)$ in powers of $x$ and $\tau$: 