New $_5F_4$ hypergeometric transformations, three-variable Mahler measures, and formulas for $1/\pi$

G. N. Watson, Three triple integrals. Quart. J. Math., Oxford Ser. 10

1939

Earlier work this paper cites.

G. S. Joyce, On the simple cubic lattice Green function. Philos. Trans. Roy. Soc. London Ser. A 273 (1973), no. 1236, 583–610

1973

Earlier work this paper cites.

B.C. Berndt, Ramanujan’s Notebooks, Part II, Springer-Verlag, New York,

1989

Earlier work this paper cites.

B.C. Berndt, Ramanujan’s Notebooks, Part III, Springer-Verlag, New York,

1991

Earlier work this paper cites.

M. L. Glasser and E. Montaldi, Staircase polygons and recurrent lattice walks, Phys. Rev. E, 48, (1993), no. 4

1993

Earlier work this paper cites.

D. W. Boyd, Mahler’s measure and special values of L-functions, Experiment. Math. 7

1994

Earlier work this paper cites.

B.C. Berndt, S. Bhargava and F.G. Garvan, Ramanujan’s theories of elliptic functions to alternative bases, Trans. Amer. Math. Soc. 347

1995

Cited alongside, same era.

B.C. Berndt, Ramanujan’s Notebooks, Part V, Springer-Verlag, New York,

1998

Cited alongside, same era.

F. Rodriguez-Villegas, Modular Mahler measures I, Topics in number theory (University Park, PA, 1997), 17–48, Math. Appl., 467, Kluwer Acad. Publ., Dordrecht, 1999

1999

Cited alongside, same era.

H. H. Chan and W. Liaw, Cubic modular equations and new Ramanujan-type series for 1 / π 1/\pi . Pacific J. Math. 192 (2000), no.2, 219–238

2000

Cited alongside, same era.

S. Ramanujan, Modular equations and approximations to π \pi , [Quart. J. Math. 45

2000

Cited alongside, same era.

H. H. Chan, S. H. Chan and Z. Liu, Domb’s numbers and Ramanujan Sato type series for 1 / π 1/\pi . Adv. Math. 186 (2004), no. 2, 396–410

2004

Later among the works it cites.

G. E. Andrews and B.C. Berndt, Ramanujan’s Lost Notebook, Part I, Springer-Verlag, New York, 2005

2005

Later among the works it cites.

M. J. Bertin, Mesure de Mahler D’Hypersurfaces K ​ 3 K3 , (Preprint 2005). See http://arxiv.org/abs/math/0501153

2005

Later among the works it cites.

G. S. Joyce and I. J. Zucker, On the evaluation of generalized Watson integrals. Proc. Amer. Math. Soc. 133 (2005), no. 1, 71-81 (electronic)

2005

Later among the works it cites.

N. Kurokawa and H. Ochiai, Mahler measures via crystalization, Commentarii Mathematici Universitatis Sancti Pauli, 54

2005

Later among the works it cites.