starting from $q(x)$ evaluated at a given order in $x$ and $\tau$ we can compute $ m^{(0,j)}(0,0) $ through (\[SP2\]) and then $q(x)$ at the next order through the set of equations (\[limz2\]),(\[eq:d40\]), (\[dev30\]),(\[eq:dev40\]) and so on. The set of equations can be solved iteratively. By this method we were able to compute the series expansion of $q(x)$ up to order $20$, improving the results of previous section.

Resummation of the expansions {#SecPad}
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Unfortunately all the expansions derived in the previous Sections are likely to be asymptotic and to obtain sensible estimates of the various quantities of interest some form of resummation must be done. Here we shall consider the standard Padè approximants which for a series of degree $N+M$ reads [@BO78]: $$P^N_M(x) = \frac{\sum_{i=0}^{N}\, a_i\, x^i}
                      {1 + \sum_{i=1}^{M}\, b_i\, x^i}$$ where the coefficients are chosen so that the first $(N+M+1)$ terms of the Taylor expansion of $P^N_M(x)$ match the the first $(N+M+1)$ terms of the of the original series. In the following we shall call this the Padè approximant $(N,M)$.

The first problem we faced is that despite the fact that the series have alternate signs, they are not Stijlties integral and therefore we cannot obtain in 