Dr. Jesús Guillera

Extraordinay prize of doctorate 2007   
THESIS  PDF



Here is the fastest of my proved formulas for pi (3 digits per term) written in a popular form. I proved it in 2002 by the WZ-method.


And here is the fastest of all my formulas for pi (5 digits per term). It has not been proved yet. I found it in 2003 using the PSLQ algorithm.




PAPERS (Arxiv)
  1. Some binomial series obtained by the WZ-method, (Accept. by D. Zeilberger). Adv. in Appl. Math., 29 - 4 (2002) pp. 599 - 603.  arXiv:math/0503345
  2. About a new kind of Ramanujan-type series, Exp. Math. 12 - 4, (2003) pp. 507 - 510.
  3. Generators of some Ramanujan formulas, The Ramanujan J. 11 - 1, (2006) pp. 41 - 48. arXiv:1104.0392
  4. A new method to obtain series for 1/pi and 1/pi2, Exp. Math. 15 - 1, (2006) pp. 83 - 89. 
  5. A class of conjectured series representations for 1/pi and 1/pi2, Exp. Math. 15 - 4, (2006) pp. 409 - 414. 
  6. Historia de las fórmulas y algoritmos para pi. La Gaceta de la RSME, 10 - 1, (2007) pp. 159 - 178. 
  7. Construction of binomial sums for pi and polylogarithmic constants inspired in BBP formulas, (with  B. Gourevitch). Appl. Math. E. Notes, (2007)   pp. 237 - 246.
  8. Hypergeometric identities for 10 extended Ramanujan-type series, The Ramanujan J. 15 - 2, (2008) pp. 219 - 234.   arXiv:1104.0396
  9. Double integrals and infinite products for some classical constants, (with J. Sondow) The Ramanujan J. 16 - 3, (2008) pp. 247 - 270. arXiv:math/0506319   
  10. Easy proofs of some Borwein's algorithms for pi. The Amer. Math. Monthly, 115 - 9, (2008) pp. 850 - 854. arXiv:0803.0991
  11. History of the formulas and algorithms for pi. Contemp. Math., 517, (2010) pp. 173 - 188. arXiv:0807.0872
  12. On WZ-pairs which prove Ramanujan series, The Ramanujan J. 22 - 3, (2008) pp. 249 - 259.  arXiv:0904.0406
  13. A matrix form of Ramanujan-type series for 1/pi. Contemp. Math., 517, (2010) pp. 189 - 206.  arXiv:0907.1547
  14. A new Ramanujan-like series for 1/pi2,  The Ramanujan J.  26, (2011), pp. 369 - 374. arXiv:1003.1915
  15. "Divergent" Ramanujan-type supercongruences. (with W. Zudilin) Proc. of the Amer. Math. Soc., 140 - 3, (2012), pp. 765 - 777. arXiv:1004.4337
  16. Mahler measure and the WZ-algorithm, (with M. Rogers). arXiv:1006.1654
  17. Mosaic supercongruences of Ramanujan-type.  Exp. Math.,  21,  (2012), pp. 65 - 68. arXiv:1007.2290
  18. Ramanujan-like series for 1/pi2 and String Theory, (with Gert Almkvist). Exp. Math. (accepted) arXiv:1009.5202
  19. WZ-proofs of "divergent" Ramanujan-type series. arXiv:1012.2681
  20. More hypergeometric identities related to Ramanujan-type series. arXiv:1104.1994
  21. Ramanujan-Sato-like series, (with G. Almkvist). arXiv:1201.5233 
  22. Kind of proofs of Ramanujan-like series.  arXiv:1203.1255 
  23. Ramanujan series upside-down, (with M. Rogers).                                                                                                                                           


PROBLEMS
  1. The Amer Math Monthly. 115 - 7, (2008) p. 665. Problem 11381. See it in the page of Jonathan Sondow (coauthor).
  2. Siam Problems,   A new formula for pi related to series of Ramanujan. Classical Analysis. Sequences and Series.  
 

MY PERSONAL JOURNAL
  1. My pi formulas PDF
  2. Series closely related to Ramanujan formulas for pi. PDF
  3. Tables of Ramanujan series with rational values of z. PDF
  4. Chains of series for 1/pi associated to WZ-pairs. PDF
  5. Expansions related to Ramanujan series and alike. PDF
  6. Collection of Ramanujan-like series for 1/pi2. PDF    
  7. Some challenging formulas for pi. PDF 


TALKS
El método WZ y las series de tipo Ramanujan para pi. PDF
Seminario Rubio de Francia. Univ de Zaragoza (11 de Marzo de 2004).
WZ-method proofs of some Ramanujan-type series for 1/pi and new series for 1/pi2. PDF
Journées Arithmet. XXIV. Marseille (July 5, 2005).
Series de Ramanujan: Generalizaciones y conjeturas. PDF
Thesis presentation. Univ de Zaragoza (2 de Julio de 2007).
Seminario teoría de números. Univ. Autónoma de Madrid (22 de Noviembre de 2007).
Ramanujan-like series for 1/pi2 and String Theory PDF
Centenario de la RSME. Palacio de congresos de Ávila. (4 de Febrero de 2011).
K-Theory, Quadratic Forms and Number Theory Seminar. School of Math. Sci. Univ. College Dublin. (Feb. 23, 2011).
Seminario Rubio de Francia. Univ de Zaragoza. (17 de Marzo de 2011)
Seminario Teoría de Números. Univ. del País Vasco, Bilbao (12 de Mayo de 2011).