Ramanujan-type 1/pi-series from bimodular forms
Journal
RAMANUJAN JOURNAL
Journal Volume
59
Journal Issue
3
Pages
831
Date Issued
2022-11
Author(s)
Wang, LQ
Abstract
We develop an approach to establish 1 / π-series from bimodular forms. Utilizing this approach, we obtain new families of 2-variable 1 / π-series associated to Zagier’s sporadic Apéry-like sequences. We first establish a general form of 1 / π-series involving constants related to the evaluation of modular forms at CM-points. Then we discuss situations when the series have rational terms. In addition, we discuss strategies for evaluating the constants involved and present a number of explicit 1 / π-series.
Subjects
Ramanujan 1/pi-series; Bimodular forms; Apery-like sequence; Hypergeometric series; CM-points; LEGENDRE POLYNOMIALS; MODULAR-FORMS; SERIES; EQUATIONS; IDENTITIES; FORMULAS; ANALOGS; NUMBERS; 1/PI
Publisher
SPRINGER
Type
journal article