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Level 17 Ramanujan–Sato series

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Abstract

Two level 17 modular functions

$$\begin{aligned} r = q^2 \prod _{n=1}^{\infty } (1-q^{n})^{\left( \frac{n}{17} \right) },\qquad s = q^{2} \prod _{n=1}^{\infty } \frac{(1 - q^{17n})^{3}}{(1-q^{n})^{3}} \end{aligned}$$

are used to construct a new class of Ramanujan–Sato series for \(1/\pi \). The expansions are induced by modular identities similar to those level of 5 and 13 appearing in Ramanujan’s Notebooks. A complete list of rational and quadratic series corresponding to singular values of the parameters is derived.

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Authors and Affiliations

  1. School of Mathematical and Statistical Sciences, University of Texas Rio Grande Valley, Edinburg, TX, 78539, USA

    Tim Huber

  2. Department of Mathematics, Pennsylvania State University, University Park, State College, PA, 16802, USA

    Daniel Schultz

  3. School of Mathematics (Zhuhai), Sun Yat-sen University, Zhuhai, 519082, Guangdong, People’s Republic of China

    Dongxi Ye

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  1. Tim Huber
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  2. Daniel Schultz
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  3. Dongxi Ye
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Correspondence to Dongxi Ye.

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The research of Dongxi Ye is partially supported by an NSF Grant DMS-1500743.

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Huber, T., Schultz, D. & Ye, D. Level 17 Ramanujan–Sato series. Ramanujan J 52, 303–322 (2020). https://doi.org/10.1007/s11139-018-0097-5

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