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This is the first article in a series devoted to the study of the asymptoticexpansions of various quantum invariants related to the twist knots. In thispaper, by using the saddle point method developed by Ohtsuki, we obtain anasymptotic expansion formula for the colored Jones polynomial of twist knots$\mathcal{K}_p$ with $p\geq 6$ at the root of unity$e^{\frac{2\pi\sqrt{-1}}{N+\frac{1}{2}}}$.

On the asymptotic expansions of various quantum invariants I: the  colored Jones polynomial of twist knots at the root of unity  $e^{\frac{2\pi\sqrt{-1}}{N+\frac{1}{2}}}$