https://ogma.newcastle.edu.au/vital/access/ /manager/Index en-au 5 https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:13147 Wed 24 Jul 2013 22:24:52 AEST ]]> https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:13362 Wed 11 Apr 2018 16:10:46 AEST ]]> https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:12926 4(± 1) are given and two new conjectures are recorded.]]> Wed 11 Apr 2018 13:49:54 AEST ]]> https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:9199 Thu 29 Mar 2018 14:30:13 AEDT ]]> https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:12944 Sat 24 Mar 2018 10:36:36 AEDT ]]> https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:13513 Sat 24 Mar 2018 10:34:54 AEDT ]]> https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:13144 Sat 24 Mar 2018 08:18:07 AEDT ]]> https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:13087 η (a,b) + R_η(b, a) = 2R_η ((a + b)/2, √ab). Alas, for some parameters the continued fraction R_η does not converge; moreover, there are converging instances where the AGM relation itself does not hold. To unravel these dilemmas we herein establish convergence theorems, the central result being that R₁ converges whenever |a| ≠|b|. Such analysis leads naturally to the conjecture that divergence occurs whenever a = be^iϕ with cos^2ϕ ≠ 1 (which conjecture has been proven in a separate work) [Borwein et al. 04b.] We further conjecture that for a/b lying in a certain—and rather picturesque—complex domain, we have both convergence and the truth of the AGM relation.]]> Sat 24 Mar 2018 08:15:36 AEDT ]]> https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:6480 Sat 24 Mar 2018 07:47:13 AEDT ]]>