# 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}
}
• Published 6 February 2012
• Mathematics
• arXiv: Combinatorics
7 Citations

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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

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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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On page 212 of his lost notebook, Ramanujan defined a new class invariant λn and constructed a table of values for λn. The paper constructs a new class of series for 1/π associated with λn. The new

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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.

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