We use skein theory to compute the coefficients of certain power series considered by Habiro in his theory of sl 2 invariants of integral homology 3-spheres. Habiro originally derived these formulas using the quantum group U q sl 2 . As an application, we give a formula for the colored Jones polynomial of twist knots, generalizing formulas of Habiro and Le for the trefoil and the figure eight knot.
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Gregor Masbaum (2003) studied this question.
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