On Ramanujan's Incomplete Elliptic Integral Identities

被引：0

作者：

Bhuvan, E. N. ^{[1
]}

机构：

[1] Natl Inst Engn Autonomous VTU, Dept Math, Mysuru 570008, Karnataka, India

来源：

INDIAN JOURNAL OF PURE & APPLIED MATHEMATICS | 2020年 / 51卷 / 04期

关键词：

Incomplete elliptic integrals; modular equations; Dedekind eta-function; theta functions; Rogers-Ramanujan continued fraction; CONTINUED-FRACTION; THEOREMS;

D O I：

10.1007/s13226-020-0493-6

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In his lost notebook, S. Ramanujan recorded incomplete elliptic integral identities of the first kind. In this paper, we give new proofs to Ramanujan's incomplete elliptic integrals of the first kind for level 5 using the parameter k(q) = R(q)R-2(q(2)), where R(q) is Rogers-Ramanujan continued fraction. Also, we construct new identities for level 5 similar to ones found in Ramanujan's work. Further, we prove related identities of level 7, using theta function identities.

引用

页码：1737 / 1751

页数：15

共 21 条

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