Generalizations of two hypergeometric sums related to conjectures of Guo
Arijit Jana, Liton Karmakar
TL;DR
This paper extends hypergeometric sum formulas related to Guo's supercongruence conjectures using the WZ-method and Zeilberger algorithm, advancing the understanding of these mathematical structures.
Contribution
It introduces new generalized formulas for hypergeometric sums, employing the WZ-method and Zeilberger algorithm, building on previous work on supercongruences.
Findings
Generalized hypergeometric sum formulas derived
New proofs of supercongruence conjectures provided
Enhanced mathematical tools for hypergeometric sums
Abstract
In 2021, the first author and Kalita obtained two general hypergeometric formulas for sums involving certain rising factorials to prove some supercongruence conjectures of Guo related to (B.2) and (C.2). In this paper, we further generalize those formulas by using the WZ-method and the Zeilberger algorithm, respectively.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAdvanced Algebra and Geometry · Advanced Mathematical Identities · Algebraic Geometry and Number Theory