PI and the AGM: A Study in Analytic Number Theory and Computational Complexity

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, results on sums of two and four squares, the transcendence of pi and Madelun2s constant, lattice sums, and elliptical invariance.Borwein, Jonathan M. is the author of 'PI and the AGM: A Study in Analytic Number Theory and Computational Complexity' with ISBN 9780471831389 and ISBN 0471831387.