Goswami, AnkushAnkushGoswamiJha, Abhash KumarAbhash KumarJhaKim, ByungchanByungchanKimOsburn, RobertRobertOsburn2025-08-282025-08-282022-04-01http://arxiv.org/abs/2204.02628v1http://repository.iitgn.ac.in/handle/IITG2025/20099We prove asymptotics and study sign patterns for coefficients in expansions of elements in the Habiro ring which satisfy a strange identity. As an application, we prove asymptotics and discuss positivity for the generalized Fishburn numbers which arise from the Kontsevich-Zagier series associated to the colored Jones polynomial for a family of torus knots. This extends Zagier's result on asymptotics for the Fishburn numbers.en-USAsymptoticsHabiro ringStrange identitiesGeneralized fishburn numberse-Printe-Print123456789/555