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We study the behaviour of the integrated density of states (IDS) $N(H^{(\\epsilon)};\\lambda)$ when $\\epsilon\\to 0$ and $\\lambda$ is a fixed energy. When $V$ is quasi-periodic (i.e. is a finite sum of complex exponentials), we prove that for each $\\lambda$ the IDS has a complete asymptotic expansion in powers of $\\epsilon$; these powers are either integer, or in some special cases half-integer. These results are new even for periodic $V$. 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