W. V. Zudilin, “Quadratic Transformations and Guillera's Formulas for $1/\pi^2$”, Mat. Zametki, 81:3 (2007), 335–340; Math. Notes, 81:3 (2007), 297

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Matematicheskie Zametki, 2007, Volume 81, Issue 3, Pages 335–340
DOI: https://doi.org/10.4213/mzm3676 (Mi mzm3676)

This article is cited in 20 scientific papers (total in 20 papers)

Quadratic Transformations and Guillera's Formulas for

1 / π^{2}

$1/\pi^2$

W. V. Zudilin^ab

^a M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
^b Steklov Mathematical Institute, Russian Academy of Sciences

Full-text PDF (404 kB) Citations (20)

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DOI: https://doi.org/10.4213/mzm3676

Abstract: We prove two new series of Ramanujan type for

1 / π^{2}

$1/\pi^2$ .

Keywords: Ramanujan-type formula, Pochhammer symbol, hypergeometric series, Apéry numbers.

Received: 11.07.2006

English version:
Mathematical Notes, 2007, Volume 81, Issue 3, Pages 297–301
DOI: https://doi.org/10.1134/S0001434607030030

Bibliographic databases:

Document Type: Article

UDC: 517.588

Language: Russian

Citation: W. V. Zudilin, “Quadratic Transformations and Guillera's Formulas for

1 / π^{2}

$1/\pi^2$ ”, Mat. Zametki, 81:3 (2007), 335–340; Math. Notes, 81:3 (2007), 297–301

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/mzm3676

https://doi.org/10.4213/mzm3676

https://www.mathnet.ru/eng/mzm/v81/i3/p335

This publication is cited in the following 20 articles:

Kam Cheong Au, “Multiple zeta values, WZ-pairs and infinite sums computations”, Ramanujan J, 66:1 (2025), 1
Kam Cheong Au, “Wilf-Zeilberger seeds and non-trivial hypergeometric identities”, Journal of Symbolic Computation, 130 (2025), 102421
Xiaojing Chen, Wenchang Chu, “TRIPLICATE DUAL SERIES OF THE DOUGALL–DIXON THEOREM”, Rocky Mountain J. Math., 54:2 (2024)
Sokal A.D., “The Euler and Springer Numbers as Moment Sequences”, Expo. Math., 38:1 (2020), 1–26
He B., J. Approx. Theory, 205 (2016), 93–101
Nayandeep Deka Baruah, Bruce C. Berndt, Heng Huat Chan, Pi: The Next Generation, 2016, 303
Gert Almkvist, Jesús Guillera, Springer Proceedings in Mathematics & Statistics, 43, Number Theory and Related Fields, 2013, 55
Nayandeep Deka Baruah, Bruce C. Berndt, Developments in Mathematics, 32, Combinatory Analysis, 2013, 15
Wadim Zudilin, Advances in Combinatorics, 2013, 287
Guillera J., Zudilin W., ““Divergent” Ramanujan-type supercongruences”, Proc. Amer. Math. Soc., 140:3 (2012), 765–777
Almkvist G., Guillera J., “Ramanujan-like series for $1/\pi^2$ and string theory”, Exp. Math., 21:3 (2012), 223–234
Almkvist G., van Straten D., Zudilin W., “Generalizations of Clausen's formula and algebraic transformations of Calabi-Yau differential equations”, Proc. Edinb. Math. Soc. (2), 54:2 (2011), 273–295
Baruah N.D., Berndt B.C., “Eisenstein series and Ramanujan-type series for $1/\pi$ ”, Ramanujan J., 23:1–3 (2010), 17–44
Chan H.H., Zudilin W., “New representations for Apéry-like sequences”, Mathematika, 56:1 (2010), 107–117
Guillera J., “History of the formulas and algorithms for $\pi$ ”, Gems in experimental mathematics, Contemp. Math., 517, eds. Amdeberhan T., Medina L., Moll V., Amer. Math. Soc., Providence, RI, 2010, 173–188
Baruah N. D., Berndt B. C., “Ramanujan's Eisenstein series and new hypergeometric-like series for $1/\pi^2$ ”, J. Approx. Theory, 160:1-2 (2009), 135–153
Baruah N.D., Berndt B.C., Chan H.H., “Ramanujan's series for $1/\pi$ : a survey”, Amer. Math. Monthly, 116:7 (2009), 567–587
Nayandeep Deka Baruah, Bruce C. Berndt, Heng Huat Chan, “Ramanujan's Series for 1/π: A Survey”, The American Mathematical Monthly, 116:7 (2009), 567
Zudilin W., “Ramanujan-type formulae for $1/\pi$ : a second wind?”, Modular forms and string duality, Fields Inst. Commun., 54, eds. Yui N., Verrill H., Doran C., Amer. Math. Soc., Providence, RI, 2008, 179–188
W. V. Zudilin, “More Ramanujan-type formulae for $1/\pi^2$ ”, Russian Math. Surveys, 62:3 (2007), 634–636

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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