Ramanujan-type series for 1/π , revisited

被引：1
|
作者：
Ye, Dongxi [1 ]
机构：
[1] Sun Yat Sen Univ, Sch Math Zhuhai, Zhuhai 519082, Guangdong, Peoples R China
来源：
CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES | 2024年 / 67卷 / 02期
关键词：
Orbifold uniformizations; (1) forward slash (pi); Clausen-type transformations; ANALOGS;
D O I：
10.4153/S0008439523000772
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this note, we revisit Ramanujan-type series for 1/pi and show how they arise from genus zero subgroups of SL2(R) that are commensurable with SL2(Z) . As illustrations, we reproduce a striking formula of Ramanujan for 1/pi and a recent result of Cooper et al., as well as derive a new rational Ramanujan-type series for 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.
引用
收藏
页码：350 / 368
页数：19
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