# Ramanujan-Sato-Like Series

@inproceedings{Almkvist2013RamanujanSatoLikeS, title={Ramanujan-Sato-Like Series}, author={G. Almkvist and Jes{\'u}s Guillera}, booktitle={Number Theory and Related Fields}, year={2013} }

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.

#### 9 Citations

Ramanujan-type formulae for $1/\pi$: The art of translation

- Mathematics
- 2013

We outline an elementary method for proving numerical hypergeometric identities, in particular, Ramanujan-type identities for $1/\pi$. The principal idea is using algebraic transformations of… Expand

Kind of proofs of Ramanujan-like series

- Mathematics
- 2012

We make a summary of the different types of proofs adding some new ideas. In addition we conjecture some relations which could be necessary in "modular type proofs" (not still found) of the… Expand

About a class of Calabi-Yau differential equations

- Mathematics
- 2013

We explain an experimental method to find CY-type differential equations of order $3$ related to modular functions of genus zero. We introduce a similar class of Calabi-Yau differential equations of… Expand

Rational Hypergeometric Ramanujan Identities for $1/\pi^c$: Survey and Generalizations

- Mathematics
- 2021

We give a simple unified proof for all existing rational hypergeometric ramanujan identities for 1/π, and give a complete survey (without proof) of several generalizations: rational hypergeometric… Expand

Arithmetic hypergeometric series

- Mathematics
- 2011

The main goal of this survey is to give common characteristics of auxiliary hypergeometric functions (and their generalisations), functions which occur in number-theoretic problems. Originally… Expand

Cutting and gluing with running couplings in $\mathcal{N}=2$ QCD

- Physics, Mathematics
- 2021

We consider the order parameter u = 〈Trφ2〉 as function of the running coupling constant τ ∈ H of asymptotically free N = 2 QCD with gauge group SU(2) and Nf ≤ 3 massive hypermultiplets. If the domain… Expand

Cutting and gluing with running couplings in N = 2 QCD

- 2021

We consider the order parameter u = 〈Trφ2〉 as function of the running coupling constant τ ∈ H of asymptotically free N = 2 QCD with gauge group SU(2) and Nf ≤ 3 massive hypermultiplets. If the domain… Expand

Výpočet Ludolfova čísla a ověření jeho vlastností

- Mathematics
- 2020

This thesis deals with analysis of available algorithms for calculating exact value of Ludolph’s number π. This thesis also describes geometric meaning, properties and brief history of Ludolph’s… Expand

Ramanujan-type $1/\pi$-series from bimodular forms

- Mathematics
- 2020

We develop an approach to establish $1/\pi$-series from bimodular forms. Utilizing this approach, we obtain new families of $2$-variable $1/\pi$-series associated to Zagier's sporadic Apery-like… Expand

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