When $\varepsilon$ is not a fixed number, but a parameter $\varepsilon\to 0$, the coefficients $f_{i_{1}...i_{n}}(y)$ are asymptotic series in $\varepsilon$ of the type $f_{i_{1}...i_{n}}(y,\varepsilon)=\sum_{j\geq 1}exp(-\lambda_{j}/\varepsilon)f_{j,i_{1}...i_{n}}$ where $\lambda_{j}\in{{\bf R}}$ , $\lambda_{1}<...<\lambda_{j}<...$, and $\lambda_{j}\to+\infty$.