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arXiv · 2403.09729

Proof and generalization of conjectures of Ramanujan Machine

Shuma Yamamoto
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Abstract

The Ramanujan Machine project predicts new continued fraction representations of numbers expressed by important mathematical constants. Generally, the value of a continued fraction is found by reducing it to a second order linear difference equation. In this paper, we prove 38 conjectures by solving the equation in two ways, use of a differential equation or application of Petkov\v{s}ek's algorithm. Especially, in the former way, we can get strong generalization of 31 conjectures.

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Shuma Yamamoto. 2024-03-13. Proof and generalization of conjectures of Ramanujan Machine. https://arxiv.org/abs/2403.09729

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