A Class of Conjectured Series Representations for $1 / \pi$
Guillera, Jesús
Experiment. Math., Tome 15 (2006) no. 1, p. 409-414 / Harvested from Project Euclid
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Using the second conjecture in the paper J. Guillera, “A New Method to Obtain Series for 1/π and 1/π2,” and inspired by the theory of modular functions, we find a method that allows us to obtain explicit formulas, involving eta or theta functions, for the parameters of a class of series for $1/ \pi$. As in J. Guillera, “A New Method to Obtain Series for 1/π and 1/π2,” the series considered in this paper include Ramanujan's series as well as those associated with the Domb numbers and Apéry numbers.
Publié le : 2006-05-14
Classification:  Ramanujan series,  series for $1/\pi$,  Domb numbers,  Apéry numbers,  Dedekind $\eta$ function,  Jacobi $\theta$ functions,  11F03 
@article{1175789776,
     author = {Guillera, Jes\'us},
     title = {A Class of Conjectured Series Representations for $1 / \pi$},
     journal = {Experiment. Math.},
     volume = {15},
     number = {1},
     year = {2006},
     pages = { 409-414},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1175789776}
}

Guillera, Jesús. A Class of Conjectured Series Representations for $1 / \pi$. Experiment. Math., Tome 15 (2006) no. 1, pp.  409-414. http://gdmltest.u-ga.fr/item/1175789776/