Year: 2026
Type: article
Abstract: Mock theta functions, introduced by Ramanujan in his last letter to Hardy, play a significant role in q-series theory and have natural connections to fractional q-calculus. In this paper, we study bilateral hypergeometric series of the form ψ22= ∑n=−∞∞(a,b;q)n(c,d;q)nzn, where (a;q)n denotes the q-shifted factorial. Using Slater’s three-term transformation formula for bilateral ψ22 series, we derive new identities for Ramanujan’s mock theta functions of orders 2, 3, 6, and 8. These transformations reveal previously unknown relationships between different q-series representations and extend the classical theory of mock theta functions within the framework of q-special functions.
Source: Fractal and Fractional
Authors: Qiuxia Hu, Bilal Khan
Institutions: Luoyang Normal University, Henan Academy of Sciences
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $3,258
Awards: G6655296550, G7164837924
OpenAlex ID: W7125786918
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