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We prove asymptotics and study sign patterns for coefficients in expansionsof elements in the Habiro ring which satisfy a strange identity. As anapplication, we prove asymptotics and discuss positivity for the generalizedFishburn numbers which arise from the Kontsevich-Zagier series associated tothe colored Jones polynomial for a family of torus knots. This extends Zagier'sresult on asymptotics for the Fishburn numbers.

Asymptotics and sign patterns for coefficients in expansions of Habiro elements