Pi: The Next Generation (eBook)

David H. Bailey currently has two affiliations for his professional research work. Dr. Bailey is Senior Scientist, Computational Research Department, Lawrence Berkeley National Laboratory from which he officially retired in June 2013 but continues as an active researcher. Since February 2013, Bailey is also a Research Fellow, Department of Computer Science, University of California, Davis.Jonathan M. Borwein is currently Laureate Professor in the School of Mathematical and Physical Sciences at the University of Newcastle (NSW) with adjunct appointments at Dalhousie and at Simon Fraser. He received his Doctorate from Oxford in 1974, and has published extensively in optimization, analysis, and computational mathematics, and has received various prizes both for research and for exposition. He directs the University of Newcastle’s Priority Research Centre in Computer Assisted Research Mathematics and its Applications (CARMA).

Foreword.- Preface.- Introduction.- Computation of pi using arithmetic-geometric mean.- Fast multiple-precision evaluation of elementary functions.- The arithmetic-geometric mean of Gauss.- The arithmetic-geometric mean and fast computation of elementary functions.- A simplified version of the fast algorithms of Brent and Salamin.- Is pi normal?.- The computation of pi to 29,360,000 decimal digits using Borweins' quartically convergent algorithm.- Gauss, Landen, Ramanujan, the arithmetic-geometric mean, ellipses, pi, and the ladies diary.- Vectorization of multiple-precision arithmetic program and 201,326,000 decimal digits of pi calculation.-Ramanujan and pi.- 11. Ramanujan, modular equations, and approximations to pi or how to compute one billion digits of pi.- Pi, Euler numbers, and asymptotic expansions.- A spigot algorithm for the digits of pi.- On the rapid computation of various polylogarithmic constants.- Similarities in irrationality proofs for pi, ln 2, ζ(2), and ζ(3).- Unbounded spigot algorithms for the digits of pi.- Mathematics by experiment: Plausible reasoning in the 21st century.- Approximations to pi derived from integrals with nonnegative integrands.- Ramanujan's series for 1/π: A survey.- The computation of previously inaccessible digits of π2 and Catalan's constant.- Walking on real numbers.- Birth, growth and computation of pi to ten trillion digits.- Pi day is upon us again and we still do not know if pi is normal.- The Life of pi.- I prefer pi: A brief mathematical history and anthology of articles in the American Mathematical Monthly.- Bibliography.- Index.