Ramanujan's last letter to Hardy introduced the world to mock theta functions, and the mock theta function identities found in Ramanujan's lost notebook added to their intriguing nature. For example, we find the four tenth-order mock theta functions and their six identities. The six identities themselves are of a spectacular nature and were first proved by Choi. Indeed, in their fifth and final volume on Ramanujan's lost notebook, Andrews and Berndt proclaimed about one of the six identities “It is inconceivable that an identity such as [Formula presented] could be stumbled upon by a mindless search algorithm without any overarching theoretical insight.” Recently, the first author discovered and proved three new tenth-order like identities but for sixth-order mock theta functions. Building on this recent discovery, we develop a long sought after overarching theoretical insight hinted at by Andrews and Berndt by finding several general families of tenth-order like identities for Appell functions, which are the building blocks of Ramanujan's mock theta functions. We underscore how this adds to the mystery of the purported missing pages of Ramanujan's lost notebook. © 2024 Elsevier Inc.
Язык оригиналаАнглийский
ЖурналJournal of Mathematical Analysis and Applications
Том537
Номер выпуска1
DOI
СостояниеОпубликовано - 1 сен 2024

ID: 117802100