Pi and the Agm
Borwein, Jonathan M / Borwein, Peter B
By examining the complex relationship between pi and the AGM, or Arithmetic-Geometric Mean, this book presents research revealing the interplay between classical analysis and modern computation and complexity theory. Two intimately-interwoven strands run through the book: the AGM iteration of Gauss, Lagrange, and Legendre, and the calculation of pi. Also included in the discussion are Rogers-Ramanujan identities, algebraic series for pi, resul...