CARMA ANALYSIS AND NUMBER THEORY SEMINAR Speaker: Laureate Prof Jon Borwein, CARMA, The University of Newcastle Title: Ramanujan's Arithmetic-Geometric Mean Continued Fractions and Dynamics (Part Two) Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle Time and Date: 3:30 pm, Wed, 10th Nov 2010 Abstract: The continued fraction: $${\cal R}_\eta(a,b) =\,\frac{{\bf \it a}}{\displaystyle \eta+\frac{\bf \it b^2}{\displaystyle \eta +\frac{4{\bf \it a}^2}{\displaystyle \eta+\frac{9 {\bf \it b}^2}{\displaystyle \eta+{}_{\ddots}}}}}$$ enjoys attractive algebraic properties such as a striking arithmetic-geometric mean relation and elegant links with elliptic-function theory. The fraction presents a computational challenge, which we could not resist. In Part II will reprise what I need from Part I and focus on the dynamics. The talks are stored here. [Permanent link]