|
|
||||
|
|
|
Last update: November 27, 2009 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Dr. Jesús Guillera Goyanes |
|
|||
|
|
|
|
||
|
Extraordinary Prize of Doctorate 2006-07 |
|
|||
|
|
|
|
||
|
|
||||
|
|
|
|
||
|
jguillera (gmail) |
|
|
||
|
|
||||
|
|
||||
Ramanujan identities. Hypergeometric series. Experimental Mathematics. Special functions. |
||||
|
|
||||
|
Here is the fastest of my proved formulas for p (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 p (5 digits per term). It has not been proved yet. I found it in 2003 using the PSLQ algorithm. |
||||
|
|
|
|
|
|
|
|
||||
|
|
||||
|
|
||||
|
PhD Thesis |
||||
|
|
||||
|
Series de Ramanujan: Generalizaciones y Conjeturas, 75 páginas PDF |
||||
|
Ramanujan Series: Generalizations and Conjectures (Thesis presentation), Univ. de Zaragoza (2-Julio-2007) PDF |
||||
|
|
||||
|
Publications ArXiv |
||||
|
|
||||
|
Some binomial series obtained by the WZ-method, Adv. in Appl. Math. 29 - 4 (2002) pp. 599-603. PDF (Accepted by Doron Zeilberger) |
||||
|
About a new kind of Ramanujan type series, Exp. Math. 12 - 4 (2003) pp. 507-510. PDF |
||||
|
Generators of some Ramanujan formulas, The Ramanujan Journal, 11 - 1 (2006) pp. 41 - 48. PDF |
||||
|
A
new method to obtain series for 1
/ p and
1 / p2
Exp.
Math. 15
- 1 (2006)
pp. 83 - 89. PDF |
||||
|
A class of conjectured series representations for 1 / p Exp. Math. 15 - 4 (2006) pp. 409 - 414. PDF |
||||
|
Historia de las fórmulas y algoritmos para p La Gaceta de la RSME, 10 - 1 (2007) pp. 159 - 178. PDF |
||||
|
Construction of binomial sums for p and polilogarithmic constants inspired by BBP formulas, Applied Mathematics E-Notes 7 - 34 (2007) |
||||
|
pp. 237 - 246. Coauthor: Boris Gourevitch. PDF |
||||
|
Hypergeometric identities for 10 extended Ramanujan-type series, The Ramanujan Journal, 15 - 2 (2008) pp. 219 - 234. PDF |
||||
|
Double integrals and infinite products for some classical constants, The Ramanujan Journal, 16 - 3 (2008) pp. 247 - 270. Coauthor: |
||||
|
Easy proofs of some Borwein's algorithms for p, The Amer. Math. Monthly, 115 - 9 (2008) pp. 850-854. PDF |
||||
|
History of the formulas and algorithms for p, Translated from the original Spanish. Updated version. PDF |
||||
|
Problem 11381 in The Amer. Math. Monthly, 115 - 7 (2008) p. 665. See it in the page of Jonathan Sondow (coauthor). |
||||
|
On WZ-pairs which prove Ramanujan series, Submitted for publication. PDF |
||||
|
A matrix form of Ramanujan-type series for 1 / p, Accepted for publication. PDF |
||||
|
|
||||
|
My personal journal (Formulas, experiments, conjectures, tables, ideas, etc) |
||||
|
|
||||
|
My pi formulas HTML PDF Tables of Ramanujan series with rational values of z PDF Series closely related to Ramanujan formulas for p PDF Chains of series for 1 / p associated to WZ-pairs PDF Expansions related to Ramanujan series and alike. PDF Three math adventures (written in 2000): Identities HTML, Near identities HTML, and RH HTML |
||||
|
|
||||
|
Talks |
||||
|
|
||||
|
El método WZ y las series de tipo Ramanujan para p, Seminario Rubio de Francia Univ. de Zaragoza (2004) PDF |
||||
|
WZ-method proofs of some Ramanujan-type series for 1 / p and new series for 1 / p 2
Journées Arithmet. XXIV
Marseille (2005)
PDF |
||||
|
Series de Ramanujan: Generalizaciones y Conjeturas, Seminario teoría de números Univ. Autónoma de Madrid (2007) PDF |
||||
|
|
||||
|
Favorite Home Pages |
||||
|
|
||||
|
|
|
|
||
|
|
|
|
|
|
|
|
|
|
|
|
|
Other mathematical links (Universities, Institutes, popularitation, tools, history, news, etc) |
||||
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
||||
|
|
||||
|
Y para variar podemos entretenernos con alguno de los estupendos videos de divulgación científica que podemos ver en Redes. |
||||
|
Otra posibilidad aún más relajante puede ser ver las bonitas fotos de los viajes de mi sobrina en La web de Guru y Jota. |
||||
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
||||