Dr. Jesús Guillera Extraordinay prize of doctorate 2007
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.
- Some binomial series obtained by the WZ-method,
Adv. in Appl. Math., 29 - 4 (2002) pp. 599 - 603. (Accepted by Doron Zeilberger).
arXiv:math/0503345
- About a new kind of Ramanujan-type series, Exp. Math. 12 - 4, (2003) pp. 507 - 510.
- Generators of some Ramanujan formulas, The Ramanujan J. 11 - 1, (2006) pp. 41 - 48. arXiv:1104.0392
- A new method to obtain series for 1/pi and 1/pi^2, Exp. Math. 15 - 1, (2006) pp. 83 - 89.
- A class of conjectured series representations for 1/pi and 1/pi^2, Exp. Math. 15 - 4, (2006) pp. 409 - 414.
- Historia de las fórmulas y algoritmos para pi. La Gaceta de la RSME, 10 - 1, (2007) pp. 159 - 178.
- Construction of binomial sums for pi and polylogarithmic constants inspired in BBP formulas, Appl. Math. E. Notes, (2007) pp. 237 - 246. Coauthor: B. Gourevitch.
- Hypergeometric identities for 10 extended Ramanujan-type series, The Ramanujan J. 15 - 2, (2008) pp. 219 - 234.
arXiv:1104.0396
- Double integrals and infinite products for some classical constants, The Ramanujan J. 16 - 3, (2008) pp. 247 - 270. Coauthor Jonathan Sondow. arXiv:math/0506319
- Easy proofs of some Borwein's algorithms for pi. The Amer. Math. Monthly, 115 - 9, (2008) pp. 850 - 854. arXiv:0803.0991
- History of the formulas and algorithms for pi. Contemp. Math., 517, (2010) pp. 173 - 188. arXiv:0807.0872
- On WZ-pairs which prove Ramanujan series, The Ramanujan J. 22 - 3, (2008) pp. 249 - 259. arXiv:0904.0406
- A matrix form of Ramanujan-type series for 1/pi. Contemp. Math., 517, (2010) pp. 189 - 206.
arXiv:0907.1547
- A new Ramanujan-like series for 1/pi^2,
The Ramanujan J.
26, (2011), pp. 369 - 374. arXiv:1003.1915
- "Divergent" Ramanujan-type supercongruences. Proc. of the Amer. Math. Soc., 140 - 3, (2012), pp. 765 - 777. Coauthor: Wadim Zudilin. arXiv:1004.4337
- Mahler measure and the WZ-algorithm. Coauthor: Mathew Rogers. arXiv:1006.1654
- Mosaic supercongruences of Ramanujan-type. arXiv:1007.2290
- Ramanujan-like series for 1/pi^2 and String Theory. Coauthor: Gert Almkvist. arXiv:1009.5202
- WZ-proofs of "divergent" Ramanujan-type series. arXiv:1012.2681
- More hypergeometric identities related to Ramanujan-type series. arXiv:1104.1994
- Ramanujan-Sato-like series.
Coauthor: Gert Almkvist. arXiv:1201.5233
- Kind of proofs of Ramanujan-like series
arXiv:1203.1255
PROBLEMS - The Amer Math Monthly. 115 - 7, (2008) p. 665. Problem 11381. See it in the page of Jonathan Sondow (coauthor).
- Siam Problems,
A new formula for pi related to series of Ramanujan. Classical Analysis. Sequences and Series.
MY PERSONAL JOURNAL - My pi formulas PDF
- Series closely related to Ramanujan formulas for pi. PDF
- Tables of Ramanujan series with rational values of z. PDF
- Chains of series for 1/pi associated to WZ-pairs. PDF
- Expansions related to Ramanujan series and alike. PDF
- Collection of Ramanujan-like series for 1/pi^2. PDF
TALKS El método WZ y las series de tipo Ramanujan para pi. WZ-method proofs of some Ramanujan-type series for 1/pi and new series for 1/pi^2. Journées Arithmet. XXIV. Marseille (2005). Series de Ramanujan: Generalizaciones y conjeturas. Thesis presentation. Univ de Zaragoza (2007). Ramanujan-like series for 1/pi^2 and String Theory
|
|
