Some new series for $1/\pi $ motivated by congruences

DOI10.4064/cm9017-2-2023arXiv2009.04379OpenAlexW4362513494MaRDI QIDQ6086107

Zhi-Wei Sun

Publication date: 9 November 2023

Published in: Colloquium Mathematicum (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2009.04379

zbMATH Keywords

symbolic computationcongruencesbinomial coefficientsRamanujan-type series for \(1/ \pi\)

Mathematics Subject Classification ID

Combinatorial identities, bijective combinatorics (05A19) Binomial coefficients; factorials; (q)-identities (11B65) Sums of squares and representations by other particular quadratic forms (11E25) Congruences; primitive roots; residue systems (11A07) Evaluation of number-theoretic constants (11Y60) Symbolic computation of special functions (Gosper and Zeilberger algorithms, etc.) (33F10)

Cites Work

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• Eisenstein series and Ramanujan-type series for \(1 / \pi\)
• Holonomic alchemy and series for \(1/\pi \)
• Legendre polynomials and Ramanujan-type series for \(1/\pi\)
• New series for powers of \(\pi\) and related congruences
• A SOLUTION OF SUN'S $520 CHALLENGE CONCERNING $\frac{520}{\pi}$
• Ramanujan's Theta Functions
• Open Conjectures on Congruences
• Some new series for $1/\pi$ and related congruences
• On Sums Related to Central Binomial and Trinomial Coefficients
• Conjectures and results on $x^2$ mod $p^2$ with $4p=x^2+dy^2$

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