________ this document in[* DVI.....]format. _________________________________________________________________ 87b:81158 (17:16) 81H20 Magnus, Alphonse (B-UCL) Asymptotic behaviour of continued fraction coefficients related to singularities of the weight function. (English) The recursion method and its applications (London, 1984), 22--45, Springer Ser. Solid-State Sci., 58, Springer, Berlin-New York, 1985. _________________________________________________________________ The local density of states $n\sb 0(E)$ is, in a known way, related to the continued fraction Green function with coefficients $a\sb n$ and $b\sb n$. Their dominant $n\to\infty$ asymptotic behaviour depends on the band structure of the support of $n\sb 0(E)$. Without [resp. with] gaps, we encounter convergence [resp. oscillations]. In this report, the isolated singularities in $n\sb 0(E)$ are tentatively related to the damped corrections to the above leading-order estimates of $a\sb n$ and $b\sb n$, $n\gg 1$. A number of examples are given and analysed via the continued fractions technique, especially in connection with an acceleration of convergence by means of the so-called ``terminators''. \{For the entire collection see MR 86g:81004.\} Reviewed by Znojil, M. (Rez) © Copyright American Mathematical Society 1987, 1995