Experimental Mathematics

A Class of Conjectured Series Representations for $1 / \pi$

Jesús Guillera

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Abstract

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.

Article information

Source
Experiment. Math., Volume 15, Issue 4 (2006), 409-414.

Dates
First available in Project Euclid: 5 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.em/1175789776

Mathematical Reviews number (MathSciNet)
MR2293592

Zentralblatt MATH identifier
1163.11031

Subjects
Primary: 11F03: Modular and automorphic functions

Keywords
Ramanujan series series for $1/\pi$ Domb numbers Apéry numbers Dedekind $\eta$ function Jacobi $\theta$ functions

Citation

Guillera, Jesús. A Class of Conjectured Series Representations for $1 / \pi$. Experiment. Math. 15 (2006), no. 4, 409--414. https://projecteuclid.org/euclid.em/1175789776


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