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| Citation: | NGUYEN Ngoc Thinh. Some applications of Dougall's 5F4 summation[J]. Journal of East China Normal University (Natural Sciences), 2017, (4): 52-63, 70. doi: 10.3969/j.issn.1000-5641.2017.04.005
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| [1] |
RAMANUJAN S. Modular equations and approximations to [J]. Quart J Math Oxford Ser, 1914, 45(2): 350-372.
|
| [2] |
BORWEIN J M, BORWEIN P B. Pi and the AGM: A Study in Analytic Number Theory and Computational Complexity [M]. New York: Wiley, 1987.
|
| [3] |
CHUDNOVSKY D V, CHUDNOVSKY G V, Approximations and complex multiplication according to Ramanu-jan [C]//Proceedings of the Centenary Conference, Urbana-Champaign, 1987. Boston: Academic Press, 1988, 375-472.
|
| [4] |
BARUAH N D, BERNDT B C. Ramanujan's series for 1/π arising from his cubic and quartic theories of elliptic functions [J]. J Math Anal Appl 2008, 341: 357-371. doi: 10.1016/j.jmaa.2007.10.011
|
| [5] |
BARUAH N D, BERNDT B C. Eisenstein Series and Ramanujan-type series for 1/π [J]. Ramanujan J, 2010, 23: 17-44. doi: 10.1007/s11139-008-9155-8
|
| [6] |
BARUAH N D, BERNDT B C, CHAN H H. Ramanujan's series for 1/π: A survey [J]. Amer Math Monthly, 2009, 116: 567-587. doi: 10.4169/193009709X458555
|
| [7] |
BARUAH N D, NAYAK N. New hypergeometric-like series for 1/π2, arising from Ramanujan's theory of elliptic functions to alternative base 3 [J]. Trans Amer Math Soc, 2011, 363: 887-900. doi: 10.1090/S0002-9947-2010-05180-3
|
| [8] |
CHAN H H, CHAN S H, LIU Z G. Domb's numbers and Ramanujan-Sato type series for 1/π [J]. Adv in Math, 2004, 186: 396-410. doi: 10.1016/j.aim.2003.07.012
|
| [9] |
CHAN H H, COOPER S, LIAW W C. The Rogers-Ramanujan continued fraction and a quintic iteration for 1/π[J]. Proc Amer Math Soc, 2007, 135(11): 3417-3425. doi: 10.1090/S0002-9939-07-09031-4
|
| [10] |
CHAN H H, LIAW W C, TAN V. Ramanujan's class invariant n and a new class of series for 1/π [J]. J London Math Soc, 2001, 64(2): 93-106.
|
| [11] |
CHAN H H, LOO K L. Ramanujan's cubic continued revisited [J]. Acta Arith, 2007, 126: 305-313. doi: 10.4064/aa126-4-2
|
| [12] |
CHAN H H, VERRILL H. The Apéry numbers, the Almkvist-Zudilin numbers and new series for 1/π [J]. Math Res Lett, 2009, 16: 405-420. doi: 10.4310/MRL.2009.v16.n3.a3
|
| [13] |
CHAN H H, RUDILIN W. New representations for Apéry-like sequences 1/π [J]. Mathematika, 2010, 56: 107-117. doi: 10.1112/S0025579309000436
|
| [14] |
CHU W. Dougall's bilateral 2H2 series and Ramanujan-like π formulas [J]. Math Comp, 2011, 80: 2223-2251. doi: 10.1090/S0025-5718-2011-02474-9
|
| [15] |
COOPER S. Series and iterations for 1/π [J]. Acta Arith, 2010, 141: 33-58. doi: 10.4064/aa141-1-2
|
| [16] |
GUILLERA J. Hypergeometric identities for 10 extended Ramanujan-type series [J]. Ramanujan J, 2008, 15:219-234. doi: 10.1007/s11139-007-9074-0
|
| [17] |
LEVRIE P. Using Fourier-Legendre expansions to derive series for 1/π and 1/π2 [J]. Ramanujan J, 2010, 22:221-230. doi: 10.1007/s11139-010-9222-9
|
| [18] |
ROGERS M. New 5F4 hypergeometric transformations, three-variable Mahler measures and formulas for 1/π[J]. Ramanujan J, 2009, 18: 327-340. doi: 10.1007/s11139-007-9040-x
|
| [19] |
ZUDILIN W. More Ramanujan-type formulae for 1/π2 [J]. Russian Math Surveys, 2007, 62 (3): 634-636. doi: 10.1070/RM2007v062n03ABEH004420
|
| [20] |
LIU Z G. A summation formula and Ramanujan type series [J]. J Math Anal App, 2012, 389: 1059-1065. doi: 10.1016/j.jmaa.2011.12.048
|
| [21] |
ANDREWS G E, ASKEY R, ROY R. Special Functions [M]. Cambridge: Cambridge University Press, 1999.
|
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