On the asymptotic expansion of various quantum invariants II: the colored Jones polynomial of twist knots at the root of unity exp(2π√−1/(N+ 1/M)) and exp(2π√−1/N)

This is the second article in a series devoted to the study of the asymptotic expansions of various quantum invariants related to the twist knots. In this article, following the method and results in [3], we present an asymptotic expansion formula for the colored Jones polynomial of twist knot K_p with p≥6 at the root of unity exp(2π√−1/(N+ 1/M)) with M≥2. Furthermore, by taking the limit M→+∞, we obtain an asymptotic expansion formula for the colored Jones polynomial of twist knots K_p with p≥6 at the root of unity exp(2π√−1/N).