Bilateral Two-Parameter Mock Theta Functions and Related Applications

Chun Wang

Department of Mathematics, Shanghai Normal University, Shanghai, 200234, P.R. China

Abstract: In this paper, we investigate new relationships for bilateral series related to two-parameter mock theta functions, which lead to many identities concerning the bilateral mock theta functions. In addition, interesting relations between the classical mock theta functions and the bilateral series are also concluded.

Keywords: mock theta functions, theta series, bilateral series, Appell–Lerch sums.

MSC: 33D15, 11F27

Received: January 20, 2025; in final form October 6, 2025; Published online October 17, 2025

Language: English

DOI: 10.3842/SIGMA.2025.087