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

Details A Matrix form of Ramanujan-type series for $1/π$ A Matrix form of Ramanujan-type series for $1/π$

2009-07-09

arxiv.org/abs/0907.1547v1

Mathematics

Number Theory

Scientific paper

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.

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