Families of multisums as mock theta functions |
| |
Institution: | Center for Combinatorics, LPMC, Nankai University, Tianjin 300071, PR China |
| |
Abstract: | In view of the Bailey lemma and the relations between Hecke-type sums and Appell–Lerch sums given by Hickerson and Mortenson, we find that many Bailey pairs given by Slater can be used to deduce mock theta functions. Therefore, by constructing generalized Bailey pairs with more parameters, we derive some new families of mock theta functions. Meanwhile, some identities between new mock theta functions and classical ones are established. Furthermore, based on the proofs of the main theorems, many q-hypergeometric transformations are obtained. |
| |
Keywords: | Bailey pairs Mock theta functions Hecke-type sums Appell–Lerch sums |
本文献已被 ScienceDirect 等数据库收录! |
|