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arXiv · 1201.5233

Ramanujan-Sato-like series

Gert Almkvist·Jesús Guillera
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Abstract

Using the theory of Calabi-Yau differential equations we obtain all the parameters of Ramanujan-Sato-like series for $1/π^2$ as $q$-functions valid in the complex plane. Then we use these q-functions together with a conjecture to find new examples of series of non-hypergeometric type. To motivate our theory we begin with the simpler case of Ramanujan-Sato series for $1/π$.

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Gert Almkvist, Jesús Guillera. 2012-10-14. Ramanujan-Sato-like series. https://arxiv.org/abs/1201.5233

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