A generalization of Zwegers' multivariable $\hat{I}¼$-function

Abstract

We introduce a one parameter deformation of Zwegers' multivariable $\hat{I}¼$-function by applying iterations of the $q$-Borel summation method, which is also a multivariate analogue of the generalized $\hat{I}¼$-function introduced by the authors. For this deformed multivariable $\hat{I}¼$-function, we give some formulas, for example, forward shift formula, translation and ${\mathfrak{S}}_{N+1}$-symmetry. Further we mention modular formulas for the Zwegers' original multivariable $\hat{I}¼$-function.

18 pages