Geodesic
Cubic and Higher Order Algorithms for π
Canadian mathematical bulletin, Tome 27 (1984) no. 4, pp. 436-443

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DOI

We show that the theory of elliptic integral transformations may be employed to construct iterative approximations for π of order p (p any prime). Details are provided for two, three and seven. The cubic case proves amenable to surprisingly complete analysis.
DOI : 10.4153/CMB-1984-067-7
Mots-clés : 10A30, 33A25, Pi, Elliptic Integrals, Algorithms, Modular Equations 
Borwein, J. M.; Borwein, P. B. Cubic and Higher Order Algorithms for π. Canadian mathematical bulletin, Tome 27 (1984) no. 4, pp. 436-443. doi: 10.4153/CMB-1984-067-7
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     title = {Cubic and {Higher} {Order} {Algorithms} for \ensuremath{\pi}},
     journal = {Canadian mathematical bulletin},
     pages = {436--443},
     year = {1984},
     volume = {27},
     number = {4},
     doi = {10.4153/CMB-1984-067-7},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1984-067-7/}
}
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