Extensions of Ramanujan's two formulas for $1/\pi$

@article{Wei2012ExtensionsOR,
  title={Extensions of Ramanujan's two formulas for \$1/\pi\$},
  author={Chuanan Wei and Dianxuan Gong},
  journal={arXiv: Combinatorics},
  year={2012}
}

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

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

$q$-analogues of several $\pi $-formulas

  • Chuanan Wei
  • Physics, Mathematics
    Proceedings of the American Mathematical Society
  • 2020
According to the $q$-series method, a short proof for Hou and Sun's identity, which is the $q$-analogue of a known $\pi$-formula, is offered. Furthermore, $q$-analogues of several other

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Using some properties of the gamma function and the well-known Gauss summation formula for the classical hypergeometric series, we prove a four-parameter series expansion formula, which can produce

Ramanujan-type formulae for 1/π: a second wind?

In 1914 S. Ramanujan recorded a list of 17 series for 1=…. We survey the methods of proofs of Ramanujan’s formulae and indicate recently discovered generalisations, some of which are not yet proven.

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We prove, by the WZ-method, some hypergeometric identities which relate ten extended Ramanujan type series to simpler hypergeometric series. The identities we are going to prove are valid for all the

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TLDR
A new kind of Ramanujan-type formula for 1/π is proposed and it is conjectured that it is related to the theory of modular functions.

New 5F4 hypergeometric transformations, three-variable Mahler measures, and formulas for 1/π

Abstract New relations are established between families of three-variable Mahler measures. Those identities are then expressed as transformations for the 5F4 hypergeometric function. We use these

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Using certain representations for Eisenstein series, we uniformly derive several Ramanujan-type series for 1/π.