Identities inspired from the Ramanujan Notebooks, first series (1998)
Simon Plouffe
TL;DR
This paper compiles formulas inspired by Ramanujan's notebooks, discovered through computational experiments using PARI-Gp, Maple, and Mathematica, including a new formula for Zeta(5).
Contribution
It introduces a collection of Ramanujan-inspired formulas obtained via symbolic computation, including a novel formula for Zeta(5).
Findings
Formulas inspired by Ramanujan's notebooks compiled.
New formula for Zeta(5) presented.
Experimental computational method used for discovery.
Abstract
I present here a collection of formulas inspired from the Ramanujan Notebooks. These formulas were found using an experimental method based on three widely available symbolic computation programs: PARI-Gp, Maple and Mathematica. A new formula is presented for Zeta(5).
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Taxonomy
TopicsAdvanced Mathematical Identities · Analytic Number Theory Research · Advanced Combinatorial Mathematics