New Proofs of Ramanujan's Identities on False Theta Functions

TL;DR

This paper presents novel proofs for five of Ramanujan's identities related to false theta functions, avoiding traditional methods like Rogers-Fine identities and Bailey transforms.

Contribution

It introduces new proof techniques for Ramanujan's false theta identities, expanding the mathematical toolkit without relying on classical identities.

Findings

Five identities on false theta functions are proved anew.

Proofs avoid Rogers-Fine identity and Bailey transforms.

Results deepen understanding of false theta functions.

Abstract

We provide new proofs to five of Ramanujan's intriguing identities on false theta functions without using the Rogers-Fine identity and Bailey transforms.