Integrals associated with Ramanujan and elliptic functions

被引：3

作者：

Berndt, Bruce C. ^{[1
]}

机构：

[1] Univ Illinois, 1409 W Green St, Urbana, IL 61801 USA

来源：

RAMANUJAN JOURNAL | 2016年 / 41卷 / 1-3期

关键词：

Definite integrals; Jacobian elliptic functions; Ramanujan's notebooks;

D O I：

10.1007/s11139-016-9793-1

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We evaluate in closed form certain classes of infinite integrals containing trigonometric and hyperbolic trigonometric functions in their integrands. Although not apparent, the integrals are related to Jacobian elliptic functions, in particular, to theorems found in Ramanujan's notebooks. One of our evaluations answers a question first posed by M. E. H. Ismail.

引用

页码：369 / 389

页数：21

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