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Pi and the AGM. A Study in Analytic Number Theory and Computational Complexity. Edition No. 1

  • ID: 2175461
  • Book
  • July 1998
  • 432 Pages
  • John Wiley and Sons Ltd
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Critical Acclaim for Pi and the AGM:

"Fortunately we have the Borwein's beautiful book . . . explores inthe first five chapters the glorious world so dear to Ramanujan . .. would be a marvelous text book for a graduate course."--Bulletinof the American Mathematical Society

"What am I to say about this quilt of a book? One is reminded ofDebussy who, on being asked by his harmony teacher to explain whatrules he was following as he improvised at the piano, replied, "Monplaisir." The authors are cultured mathematicians. They haveselected what has amused and intrigued them in the hope that itwill do the same for us. Frankly, I cannot think of a moreprovocative and generous recipe for writing a book . . . (it) iscleanly, even beautifully written, and attractively printed andcomposed. The book is unique. I cannot think of any other book inprint which contains more than a smidgen of the material theseauthors have included.--SIAM Review

"If this subject begins to sound more interesting than it did inthe last newspaper article on 130 million digits of Pi, I havepartly succeeded. To succeed completely I will have gotten youinterested enough to read the delightful and important book by theBorweins."--American Mathematical Monthly

"The authors are to be commended for their careful presentation ofmuch of the content of Ramanujan's famous paper, 'Modular Equationsand Approximations to Pi'. This material has not heretoforeappeared in book form. However, more importantly, Ramanujanprovided no proofs for many of the claims that he made, and so theauthors provided many of the missing details . . . The Borweins,indeed have helped us find the right roads."--Mathematics ofComputation
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Complete Elliptic Integrals and the Arithmetic-Geometric MeanIteration.

Theta Functions and the Arithmetic-Geometric Mean Iteration.

Jacobi's Triple-Product and Some Number TheoreticApplications.

Higher Order Transformations.

Modular Equations and Algebraic Approximations to pi.

The Complexity of Algebraic Functions.

Algorithms for the Elementary Functions.

General Means and Iterations.

Some Additional Applications.

Other Approaches to the Elementary Functions.

Pi.

Bibliography.

Symbol List.

Index.
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Jonathan M. Borwein
Peter B. Borwein
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