Abstract
Abstract
In this note, we revisit Ramanujan-type series for
$\frac {1}{\pi }$
and show how they arise from genus zero subgroups of
$\mathrm {SL}_{2}(\mathbb {R})$
that are commensurable with
$\mathrm {SL}_{2}(\mathbb {Z})$
. As illustrations, we reproduce a striking formula of Ramanujan for
$\frac {1}{\pi }$
and a recent result of Cooper et al., as well as derive a new rational Ramanujan-type series for
$\frac {1}{\pi }$
. As a byproduct, we obtain a Clausen-type formula in some general sense and reproduce a Clausen-type quadratic transformation formula closely related to the aforementioned formula of Ramanujan.
Publisher
Canadian Mathematical Society
Cited by
1 articles.
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1. On Ramanujan's inversion formulas;Journal of Mathematical Analysis and Applications;2024-07