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arXiv · 2410.19289

The Modularity of Z.-W. Sun's Conjectural Formulas for $\frac{1}{\pi}$

Mark van Hoeij·Wei-Lun Tsai·Dongxi Ye
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Abstract

In this work, we establish modular parameterizations for two general formulas for $\frac{1}{\pi}$ that subsume conjectural Ramanujan type formulas due to Z.-W. Sun, which have remained open since 2011. As an application of this, in a conceptual way we interpret how Sun's conjectural formulas arise and can be verified, as well as recover other cases that were proved by Cooper, Wan and Zudilin.

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Mark van Hoeij, Wei-Lun Tsai, Dongxi Ye. 2024-10-25. The Modularity of Z.-W. Sun's Conjectural Formulas for $\frac{1}{\pi}$. https://arxiv.org/abs/2410.19289

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