7 papers
A degeneration of the generalized Zwegers' -function according to the Ramanujan difference equation
G. Shibukawa, S. Tsuchimi
In this paper, we introduce the little -function, which is obtained as a degenerate limit of the generalized -function. We derive the little -function as the image of the…
Degenerations of the fourth order -Garnier system arising from confluences in quivers
Kazuya Matsugashita, Takao Suzuki, Satoshi Tsuchimi
The -Garnier system was first proposed by Sakai, and alternative directions for its discrete time evolutions were provided by Nagao and Yamada. Recently, it was shown that all o…
A generalization of Zwegers' multivariable -function
G. Shibukawa, S. Tsuchimi
We introduce a one parameter deformation of Zwegers' multivariable -function by applying iterations of the -Borel summation method, which is also a multivariate analogue of t…
A solution in terms of mock modular forms for the -Painlevé equation of the type
Satoshi Tsuchimi
We present a solution of the -Painlevé equation in terms of the -function. The -function introduced by Zwegers is the most fundamental object in the stud…
-difference equations satisfied by the universal mock theta functions
Satoshi Tsuchimi
In this paper, we give fundamental solutions of some -difference equations satisfied by the universal mock theta functions and the higher level Appell functions. As an applicati…
The generalized Zwegers' -function and transformation formulas for the bilateral basic hypergeometric series
Genki Shibukawa, Satoshi Tsuchimi
By applying Slater's transformation formulas for the bilateral basic hypergeometric series , we derive three type translation formulas for the generalized Zwegers' -f…
A Generalization of Zwegers' -Function According to the -Hermite-Weber Difference Equation
Genki Shibukawa, Satoshi Tsuchimi
We introduce a one parameter deformation of the Zwegers' -function as the image of -Borel and -Laplace transformations of a fundamental solution for the -Hermite-Weber…