Ramanujan-Sato-like series

Abstract

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 $1/\pi$.

The Addendum is new

References in corpus (5)

• Ramanujan-type supercongruences
• Quadratic transformations and Guillera's formulae for $1/{\pi }^2$
• On Sp_4 modularity of Picard--Fuchs differential equations for Calabi--Yau threefolds (with an appendix by Vicentiu Pasol)
• The art of finding Calabi-Yau differential eq1uations
• Transformations of Jesus Guillera's formulas for 1/Pi^2

Cited by in corpus (2)

• Rational Hypergeometric Ramanujan Identities for $1/{\pi }^c$: Survey and Generalizations
• About a class of Calabi-Yau differential equations