$\lambda $ as an index, but will often use $\mu $ in symbol computations. Some formulas from [@GSc] and some immediate consequences are collected in Appendices A and B, to which we refer in the following.

As mentioned already, the proof in [@GSc] of the expansion (1.10) for $A=G$ is straightforwardly modified to allow $\nu \notin\Bbb Z$. For an analysis of the coefficients, we apply a partition of unity $1=\sum_{i=1}^{i_0}\theta _i$ subordinate to a cover of $X$ by coordinate patches $U _j$, $j=1,\dots,j_0$, with trivializations $\psi _j\:E|_{U_j}\to V_j\times
\Bbb C^{\operatorname{dim}E}$, $V_j\subset\subset \crnp$, $U_j\cap
\partial X$ mapped into $\partial \crnp$, such that any two of the functions $\theta _{i_1}$ and $\theta _{i_2}$ are supported in one of the coordinate patches $U _{j(i_1,i_2)}$. Replacing $G$ by $\sum_{i_1,i_2\le i_0}\theta _{i_1}G\theta _{i_2}$, we find from $GQ^N_{\lambda ,+}$ and $GG^{(N)}_\lambda
$ a system of terms $$G=\sum_{i_1,i_2\le i_0}(\theta _{i_1}G\theta _{i_2}Q^N_{\lambda ,+}+
\theta _{i_1}G\theta
_{i_2}G^{(N)}_\lambda ),\tag3.1$$ where $\theta _{i_1}$ and $\theta _{i_2}$ are supported either in an interior coordinate patch (with closure in the interior) or a patch meeting the boundary, and we can study each term in the local coordinates. Since $\theta _{i_2}G^{(N)}_\lambda $ is strongly polyhomogeneous of order $-\infty $ when $\theta _{i_2}$ is supported 