A further $q$-analogue of a formula due to Guillera
| Title: | A further $q$-analogue of a formula due to Guillera |
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| Authors: | Campbell, John M. |
| Publication Year: | 2024 |
| Collection: | Mathematics |
| Subject Terms: | Mathematics - Combinatorics, 05A30 |
| More Details: | Hou, Krattenthaler, and Sun have introduced two $q$-analogues of a remarkable series for $\pi^2$ due to Guillera, and these $q$-identities were, respectively, proved with the use of a $q$-analogue of a Wilf-Zeilberger pair provided by Guillera and with the use of ${}_{3}\phi_{2}$-transforms. We prove a $q$-analogue of Guillera's formula for $\pi^2$ that is inequivalent to previously known $q$-analogues of the same formula due to Guillera, including the Hou-Krattenthaler-Sun $q$-identities and a subsequent $q$-identity due to Wei. In contrast to previously known $q$-analogues of Guillera's formula, our new $q$-analogue involves another free parameter apart from the $q$-parameter. Our derivation of this new result relies on the $q$-analogue of Zeilberger's algorithm. |
| Document Type: | Working Paper |
| Access URL: | http://arxiv.org/abs/2407.00621 |
| Accession Number: | edsarx.2407.00621 |
| Database: | arXiv |
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