Mathematics Commons^™

Asymptotics And Sign Patterns For Coefficients In Expansions Of Habiro Elements, Ankush Goswami, Abhash Kumar Jha, Byungchan Kim, Robert Osburn

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

We 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.