PUBLISHED WORKS

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Published papers

2002

• Some binomial series obtained by the WZ-method. Adv. in Appl. Math. 29 (2002), no. 4, 599-603.
  Links: arXiv:math/0503345, journal.
   

2003

• About a new kind of Ramanujan-type series. Experiment. Math. 12 (2003), no. 4, 507-510.
  Links: journal.
   

2006

• Generators of some Ramanujan formulas. Ramanujan J. 11 (2006), no. 1, 41-48
  Links: arXiv:1104.0392, journal.
   
• A new method to obtain series for 1/pi and 1/pi². Experiment. Math. 15 (2006), no. 1, 83-89.
  Links: journal.
   
• A class of conjectured series representations for 1/pi. Experiment. Math. 15 (2006), no. 4, 409-414.
  Links: journal.
   

2007

• Historia de las fórmulas y algoritmos para pi. Gac. R. Soc. Mat. Esp. 10 (2007), no. 1, 159-178.
  Links: journal.
   
• Construction of binomial sums for pi and polylogarithmic constants inspired by BBP formulas, with Boris Gourévitch. Appl. Math. E-Notes 7 (2007), 237-246.
  Links: journal.
   

2008

• Hypergeometric identities for 10 extended Ramanujan-type series. Ramanujan J. 15 (2008), no. 2, 219-234.
  Links: arXiv:1104.0396, journal.
   
• Double integrals and infinite products for some classical constants via analytic continuations of Lerch's transcendent, with Jonathan Sondow. Ramanujan J. 16 (2008), no. 3, 247-270.
  Links: arXiv:math/0506319, journal.
   
• Easy proofs of some Borwein algorithms for pi. Amer. Math. Monthly 115 (2008), no. 9, 850-854.
  Links: arXiv:0803.0991, journal.
   

2010

• On WZ-pairs which prove Ramanujan series. Ramanujan J. 22 (2010), no. 3, 249-259.
  Links: arXiv:0904.0406, journal.
   
• History of the formulas and algorithms for pi. Gems in experimental mathematics, 173-188, Contemp. Math., 517, Amer. Math. Soc., Providence, RI, 2010.
  Links: arXiv:0807.0872, journal.
   
• A matrix form of Ramanujan-type series for 1/pi. Gems in experimental mathematics, 189-206, Contemp. Math., 517, Amer. Math. Soc., Providence, RI, 2010.
  Links: journal.
   

2011

• A new Ramanujan-like series for 1/pi². Ramanujan J. 26 (2011), no. 3, 369-374.
  Links: arXiv:1003.1915, journal.
   

2012

• “Divergent” Ramanujan-type supercongruences, with Wadim Zudilin. Proc. Amer. Math. Soc. 140 (2012), no. 3, 765-777.
  Links: arXiv:1004.4337, journal.
   
• Mosaic supercongruences of Ramanujan type. Exp. Math. 21 (2012), no. 1, 65-68.
  Links: arXiv:1007.2290, journal.
   
• Ramanujan-like series for 1/pi² and string theory, with Gert Almkvist. Exp. Math. 21 (2012), no. 3, 223-234.
  Links: arXiv:1009.5202, journal.
   

2013

• Ramanujan-Sato-like series, with Gert Almkvist. Number theory and related fields, 55-74, Springer Proc. Math. Stat., 43, Springer, New York, 2013.
  Links: arXiv:1201.5233, journal.
   
• More hypergeometric identities related to Ramanujan-type series. Ramanujan J. 32 (2013), no. 1, 5-22.
  Links: arXiv:1104.1994, journal.
   
• Ramanujan-type formulae for 1/pi: the art of translation, with Wadim Zudilin. The legacy of Srinivasa Ramanujan, 181-195, Ramanujan Math. Soc. Lect. Notes Ser., 20, Ramanujan Math. Soc., Mysore, 2013.
  Links: arXiv:1302.0548.
   
• WZ-proofs of “divergent” Ramanujan-type series. Advances in combinatorics, 187-195, Springer, Heidelberg, 2013.
  Links: arXiv:1012.2681, journal.
   

2014

• Ramanujan series upside-down, with Mathew Rogers. J. Aust. Math. Soc. 97 (2014), no. 1, 78-106.
  Links: arXiv:1206.3981, journal.
   

2015

• A family of Ramanujan-Orr formulas for 1/pi. Integral Transforms Spec. Funct. 26 (2015), no. 7, 531-538.
  Links: arXiv:1501.06413, journal.
   
• Mahler measure and the WZ algorithm, with Mathew Rogers. Proc. Amer. Math. Soc. 143 (2015), no. 7, 2873-2886.
  Links: arXiv:1006.1654, journal.
   

2016

• New proofs of Borwein-type algorithms for Pi. Integral Transforms Spec. Funct. 27 (2016), no. 10, 775-782.
  Links: arXiv:1604.00193, journal.
   

2017

• More Ramanujan-Orr formulas for 1/pi. New Zealand J. Math. 47 (2017), 151-160.
  Links: journal.
   

2018

• Crouching AGM, hidden modularity, with Shaun Cooper, Armin Straub and Wadim Zudilin. Frontiers in orthogonal polynomials and q-series, 169-187, Contemp. Math. Appl. Monogr. Expo. Lect. Notes, 1, World Sci. Publ., Hackensack, NJ, 2018.
  Links: arXiv:1604.01106, journal.
   
• Dougall's ₅F₄ sum and the WZ algorithm. Ramanujan J. 46 (2018), no. 3, 667-675.
  Links: arXiv:1611.04385, journal.
   
• Self-replication and Borwein-like algorithms. Ramanujan J. 47 (2018), no. 2, 447-455.
  Links: arXiv:1702.05378, journal.
   
• Proofs of some Ramanujan series for 1/pi using a program due to Zeilberger. J. Difference Equ. Appl. 24 (2018), no. 10, 1643-1648.
  Links: arXiv:1804.02695, journal.
   

2019

• WZ pairs and q-analogues of Ramanujan series for 1/pi. J. Difference Equ. Appl. 24 (2018), no. 12, 1871-1879.
  Links: arXiv:1803.08477, journal.
   
• Ramanujan series with a shift. J. Aust. Math. Soc. 107 (2019), no. 3, 367-380.
  Links: arXiv:1802.02023, journal.
   

2020

• When Ramanujan meets Fibonacci and Lucas. Amer. Math. Monthly 127 (2020), no. 2, 159.
  Links: journal (filler 1 page).
   
• A method for proving Ramanujan's series for 1/pi. Ramanujan J. 52 (2020), no. 2, 421-431.
  Links: arXiv:1807.07394, journal.
   
• Bilateral Ramanujan-like series for 1/pi^k and their congruences. Int. J. Number Theory 16 (2020), no. 9, 1969-1988.
  Links: arXiv:1908.05123, journal.
   
• Las series para 1/pi de S. Ramanujan. Gac. R. Soc. Mat. Esp. 23 (2020), no. 3, 487-506.
  Links: journal.
   

2021

• Proof of a rational Ramanujan-type series for 1/pi. The fastest one in level 3. Int. J. Number Theory 17 (2021), no. 2, 473-477.
  Links: arXiv:1811.01200, journal.
   
• Proof of Chudnovsky' hypergeometric series for 1/pi using Weber modular polynomials. Transcendence in algebra, combinatorics, geometry and number theory, 341-354, Springer Proc. Math. Stat., Springer, 373, Springer, 2021.
  Links: arXiv:2003.06668, journal.
   

2024

• Heuristic derivation of Zudilin's supercongruences for rational Ramanujan series. Revista Matemática Complutense, published online.
  Links: arXiv:2312.16827, journal.
   
• Ramanujan's series for 1/pi. Encyclopaedia of Srinivasa Ramanujan and His Mathematics, to appear.
   

Published problems

• An infinite product for the exponential, with Jonathan Sondow. Problem 11381. Amer. Math. Monthly 115 (2008), no. 7, p. 665.
  Links: web of J. Sondow, journal.
   
• A new formula for pi related to series of Ramanujan. Problem 11-003, LINK. Solution with Mathew Rogers (equation (62) in LINK). SIAM Problems and Solutions, CA, Sequences and Series.