Mathematics – Number Theory
Scientific paper
2012-01-25
Mathematics
Number Theory
An example of a complex series for $1/\pi^2$ is added
Scientific paper
Using the theory of Calabi-Yau differential equations we obtain all the
parameters of Ramanujan-Sato-like series for $1/\pi^2$ 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 $1/\pi$.
Almkvist Gert
Guillera Jesus
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