- Title
- A cubic counterpart of Jacobi's identity and the AGM
- Creator
- Borwein, J. M.; Borwein, P. B.
- Relation
- Transactions of the American Mathematical Society Vol. 323, Issue 2, p. 691-701
- Publisher Link
- http://dx.doi.org/10.1090/S0002-9947-1991-1010408-0
- Publisher
- American Mathematical Society
- Resource Type
- journal article
- Date
- 1991
- Description
- We produce exact cubic analogues of Jacobi's celebrated theta function identity and of the arithmetic-geometric mean iteration of Gauss and Legendre. The iteration in question is an+1 := an + 2bn / 3 and bn+1 := [formula cannot be replicated]. The limit of this iteration is identified in terms of the hypergeometric function ₂F₁ (1/3, 2/3; 1 ; ·), which supports a particularly simple cubic transformation.
- Subject
- mean iterations; theta functions; hypergeometric functions; generalised elliptic functions; cubic transformations; pi; Ramanujan
- Identifier
- http://hdl.handle.net/1959.13/940514
- Identifier
- uon:13030
- Identifier
- ISSN:0002-9947
- Rights
- First published in Transactions of the American Mathematical Society in Vol. 323, No. 2, pp. 691-701, 1991, published by the American Mathematical Society
- Language
- eng
- Full Text
- Reviewed
- Hits: 4501
- Visitors: 5851
- Downloads: 605
| Thumbnail | File | Description | Size | Format | |||
|---|---|---|---|---|---|---|---|
| View Details Download | ATTACHMENT01 | Publisher version (open access) | 777 KB | Adobe Acrobat PDF | View Details Download |