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Mat. Zametki, 2007, Volume 81, Issue 3, Pages 335–340 (Mi mz3676)  

This article is cited in 11 scientific papers (total in 11 papers)

Quadratic Transformations and Guillera's Formulas for $1/\pi^2$

W. V. Zudilinab

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

Abstract: We prove two new series of Ramanujan type for $1/\pi^2$.

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

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

Full text: PDF file (404 kB)
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English version:
Mathematical Notes, 2007, 81:3, 297–301

Bibliographic databases:

UDC: 517.588
Received: 11.07.2006

Citation: 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), 297–301

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. W. V. Zudilin, “More Ramanujan-type formulae for $1/\pi^2$”, Russian Math. Surveys, 62:3 (2007), 634–636  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    2. 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  mathscinet  zmath  isi
    3. 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  crossref  mathscinet  zmath  isi  elib  scopus
    4. 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  crossref  mathscinet  zmath  isi  elib
    5. Baruah N.D., Berndt B.C., “Eisenstein series and Ramanujan-type series for $1/\pi$”, Ramanujan J., 23:1–3 (2010), 17–44  crossref  mathscinet  zmath  isi  scopus
    6. Chan H.H., Zudilin W., “New representations for Apéry-like sequences”, Mathematika, 56:1 (2010), 107–117  crossref  mathscinet  zmath  isi  elib  scopus
    7. 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  crossref  mathscinet  zmath  isi
    8. 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  crossref  mathscinet  zmath  isi  scopus
    9. Guillera J., Zudilin W., ““Divergent” Ramanujan-type supercongruences”, Proc. Amer. Math. Soc., 140:3 (2012), 765–777  crossref  mathscinet  zmath  isi  elib  scopus
    10. Almkvist G., Guillera J., “Ramanujan-like series for $1/\pi^2$ and string theory”, Exp. Math., 21:3 (2012), 223–234  crossref  mathscinet  zmath  isi  elib  scopus
    11. He B., J. Approx. Theory, 205 (2016), 93–101  crossref  mathscinet  zmath  isi  elib  scopus
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