Mock theta functions admit a unique resurgent continuation across their natural boundary, with the continuation fixed by their Mordell-Appell integrals via rotated Laplace contours.
Maass, Lal, S.,Lectures on Modular Functions of One Complex Variable, Springer
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On Uniqueness of Mock Theta Functions
Mock theta functions admit a unique resurgent continuation across their natural boundary, with the continuation fixed by their Mordell-Appell integrals via rotated Laplace contours.