A geometric view of rational landen transformations

Bulletin of the London Mathematical Society

Volumn 35, Issue 3, 2003, Pages 293-301

  Hubbard, John ^a   Moll, Victor ^b  

^a Cornell University ^*  (United States)

^b Tulane University   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0038116787     PISSN: 00246093     EISSN: None     Source Type: Journal    
DOI: 10.1112/S0024609303001930     Document Type: Article

References (8)

1. G. BOROS and V. MOLL, 'A rational Landen transformation. The case of degree six', Contemp. Math. 251 (2000) 83-91.
2. G. BOROS and V. MOLL, 'Landen transformation and the integration of rational functions', Math. Comp. 71 (2001) 649-668.
3. P. BORWEIN and J. BORWEIN, Pi and the AGM. A study in analytic number theory and computational complexity, Canad. Math. Soc. Ser. Monogr. Adv. Texts (Wiley, New York, 1987).
4. C. F. GAUSS, 'Arithmetische Geometrisches Mittel', Werke vol. 3 (Königliche Gesellschaft der Wissenschaften, Gottingen, 1799) 361-432 (Reprinted by Olms, Hildescheim, 1981).
5. D. GRAYSON, 'The arithogeometric mean', Arch. Math. 52 (1989) 507-512.
6. J. LANDEN, 'A disquisition concerning certain fluents, which are assignable by the arcs of the conic sections; wherein are investigated some new and useful theorems for computing such fluents', Philos. Trans. Royal Soc. London 61 (1771) 298-309.
7. J. LANDEN, 'An investigation of a general theorem for finding the length of any arc of any conic hyperbola, by means of two elliptic arcs, with some other new and useful theorems deduced therefrom', Philos. Trans. Royal Soc. London 65 (1775) 283-289.
8. H. McKEAN and V. MOLL, Elliptic curves: function theory, geometry, arithmetic (Cambridge University Press, 1997).