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.
