A Matrix form of Ramanujan-type series for $1/\pi$

Jesus Guillera

A Matrix form of Ramanujan-type series for $1/\pi$

Number Theory 2009-07-10 v1

Authors: Jesus Guillera

Abstract

In this paper we prove theorems related to the Ramanujan-type series for $1/\pi$ (type $_3F_2$ ) and to the Ramanujan-like series, discovered by the author, for $1/\pi^2$ (type $_5F_4$ ). Our developments for the cases $_3 F_2$ and $_5 F_4$ connect with the theory of modular functions and with the theory of Calabi-Yau differential equations, respectively.

Keywords

Ramanujan-type series 1/pi modular functions Calabi-Yau differential equations hypergeometric series

Cite

@article{arxiv.0907.1547,
  title  = {A Matrix form of Ramanujan-type series for $1/\pi$},
  author = {Jesus Guillera},
  journal= {arXiv preprint arXiv:0907.1547},
  year   = {2009}
}

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