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We prove several asymptotic results for partial and false theta functionsarising from Jacobi forms, as the modular variable $\tau$ tends to $0$ alongthe imaginary axis, and the elliptic variable $z$ is unrestricted in thecomplex plane. We observe that these functions exhibit Stokes' phenomenon - theasymptotic behavior of these functions sharply differs depending on where theelliptic variable $z$ is located within the complex plane. We apply our resultsto study the asymptotic expansions of regularized characters and quantumdimensions of the $(1,p)$-singlet vertex operator algebra coming from conformalfield theory. This, in particular, recovers and extends several known resultspertaining to regularized quantum dimensions, which served as a main source ofmotivation.

Asymptotic behavior of partial and false theta functions arising from Jacobi forms and regularized characters