Proofs of some conjectures of Merca on truncated series involving the Rogers-Ramanujan functions

In 2012, Andrews and Merca investigated the truncated version of the Euler pentagonal number theorem. Their work has opened up a new study on truncated theta series and has inspired several mathematicians to work on the topic. In 2019, Merca studied the Rogers-Ramanujan functions and posed three groups of conjectures on truncated series involving the Rogers-Ramanujan functions. In this paper, we present a uniform method to prove the three groups of conjectures given by Merca based on a result due to P & oacute;lya and Szeg & ouml;. (c) 2024 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar