A NEW -ANALOGUE OF VAN HAMME’S (A.2) SUPERCONGRUENCE
| Autor: | Victor J. W. Guo |
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| Rok vydání: | 2022 |
| Předmět: | |
| Zdroj: | Bulletin of the Australian Mathematical Society. 107:22-30 |
| ISSN: | 1755-1633 0004-9727 |
| DOI: | 10.1017/s0004972722000478 |
| Popis: | We give a new q-analogue of the (A.2) supercongruence of Van Hamme. Our proof employs Andrews’ multiseries generalisation of Watson’s $_{8}\phi _{7}$ transformation, Andrews’ terminating q-analogue of Watson’s $_{3}F_{2}$ summation, a q-Watson-type summation due to Wei–Gong–Li and the creative microscoping method, developed by the author and Zudilin [‘A q-microscope for supercongruences’, Adv. Math.346 (2019), 329–358]. As a conclusion, we confirm a weaker form of Conjecture 4.5 by the author [‘Some generalizations of a supercongruence of van Hamme’, Integral Transforms Spec. Funct.28 (2017), 888–899]. |
| Databáze: | OpenAIRE |
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