Generalizations of some q-product identities of Ramanujan and others

Authors

Timothy J. Huber, The University of Texas Rio Grande ValleyFollow
James McLaughlin, West Chester University of Pennsylvania
Dongxi Ye, Sun Yat-sen UniversityFollow

Document Type

Book Chapter

Publication Date

2025

Abstract

By considering certain limiting cases of a WP-Bailey chain discovered by Andrews, and also limiting cases of certain classical summation formulae for basic hypergeometric series, we derive new expressions for certain Lambert series in terms of basic hypergeometric series. In some cases, the resulting series involve an arbitrary Bailey pair. This allows for the derivation of new basic hypergeometric expansions for some q-products and series that Ramanujan expressed in terms of Lambert series. Some of Ramanujan’s identities are extended to more general relations containing one or more free parameters.

Comments

Original published version available at https://doi.org/10.1090/conm/819/16397

Recommended Citation

Huber, T., McLaughlin, J., & Ye, D. (2025). Generalizations of some 𝑞-product identities of Ramanujan and others. In H. S. Cohl, R. S. Costas-Santos, & R. S. Maier (Eds.), Applications and q-Extensions of Hypergeometric Functions (Vol. 819, pp. 255–268). American Mathematical Society. https://doi.org/10.1090/conm/819/16397

First Page

255

Last Page

268

Publication Title

Applications and Q-Extensions of Hypergeometric Functions

DOI

10.1090/conm/819/16397