TY - JOUR

T1 - Splitting Appell functions in terms of single quotients of theta functions

AU - Mortenson, E.T.

AU - Urazov, D.

N1 - Export Date: 21 March 2024 Адрес для корреспонденции: Mortenson, E.T.; Department of Mathematics and Computer Science, Russian Federation; эл. почта: etmortenson@gmail.com Сведения о финансировании: Foundation for the Advancement of Theoretical Physics and Mathematics, 20-7-1-25-1 Текст о финансировании 1: We would like to thank Dean Hickerson for his helpful comments and suggestions. This work was supported by the Theoretical Physics and Mathematics Advancement Foundation BASIS, agreement No. 20-7-1-25-1.

PY - 2024/9/1

Y1 - 2024/9/1

N2 - 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.

AB - 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.

KW - Appell functions

KW - Mock theta functions

KW - Theta functions

UR - https://www.mendeley.com/catalogue/71e2ade4-8972-3224-8140-3c105a67ea9d/

U2 - 10.1016/j.jmaa.2024.128261

DO - 10.1016/j.jmaa.2024.128261

M3 - статья

VL - 537

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

SN - 0022-247X

IS - 1

ER -