Bibliography of the ISC

by Simon Plouffe CECM

D. H. Bailey, P. B. Borwein and S. Plouffe, On The Rapid Computation of Various Polylogarithmic Constants , preprint, 1996. To be published in Mathematics of Computation.

J. M. Borwein and P. B. Borwein, Pi and the AGM: A Study in Analytic Number Theory and Computational Complexity}, John Wiley, New York, 1987.

David H. Bailey, The Computation of to 29,360,000 Decimal Digits Using Borweins' Quartically Convergent Algorithm

H. R. P. Ferguson and D. H. Bailey, Analysis of PSLQ, An Integer Relation Algorithm, manuscript, 1996. Available from author.

D. E. Knuth, The Art of Computer Programming ,vol. 2, Addison-Wesley, Reading, MA, 1981.

D. Shanks and J. W. Wrench, Calculation of Pi to 100,000 Decimals, in Mathematics of Computation, vol. 16 (1962), pg. 76--79. Table of 100,265 digits of Pi.

Henrici, Peter Elements of numerical analysis. John Wiley & Sons, Inc., New York-London-Sydney 1964 xv+328 pp.

Milton Abramowitz and Irene A. Stegun. Handbook of mathematical functions with formulas, graphs, and mathematical tables. Edited by Reprint of the 1972 edition. Dover Publications, Inc.,New York, 1992. xiv+1046 pp. ISBN: 0-486-61272-4

Hansen, Eldon Sums of functions satisfying recursion relations. Amer. Math. Monthly 88 (1981), no. 9, 676--679.

Hansen, Eldon, A table of series and products, Englewood Cliffs, N.J. : Prentice-Hall, (1975), 523 p. This book contains more than 5000 formulas.

A Polynomial Time,Numerically Stable Integer Relation Algorithm,by R. Helaman,P.Ferguson and D.H.Bailey RNR Technical Report RNR-91-032 December,1991

Allouche, Jean-Paul; Arnold, André; Berstel, Jean; Brlek, Sre\v cko; Jockusch, William; Plouffe, Simon; Sagan, Bruce E. A relative of the Thue-Morse sequence. Formal power series and algebraic combinatorics (Montreal, PQ, 1992). Discrete Math. 139 (1995), no. 1-3, 455--461.

Sloane, N. J. A.; Plouffe, Simon The encyclopedia of integer sequences. With a separately available computer disk. Academic Press, Inc., San Diego, CA, 1995. xiv+587 pp. ISBN: 0-12-558630-2

Bergeron, François; Plouffe, Simon , Computing the generating function of a series given its first few terms. Experiment. Math. 1 (1992), no. 4, 307--312.

Pour la Science, french version of Scientific American,September 1994, page 25.

The Quest for Pi, Peter Borwein, Jon Borwein, David H. Bailey, Simon Plouffe, preprint 1996.

Program: GFUN , a maple package, in collaboration with François Bergeron (UQAM), Bruno Salvy and Paul Zimmermann . Most of the program was actually written by Salvy and Zimmermann.

A method to find the Algebraic Generating Function from a series. SFCA 93, Florence, Italy, pp. 355-377. Proceedings of the 5th conference on Formal Power Series and Algebraic Combinatorics.

Borwein, Jonathan, and Peter Borwein. 1990. A Dictionary of Real Numbers. Pacific Grove, Calif.: Wadsworth & Brooks/Cole.

R. E. Crandall, Topics in Advanced Scientific Computation, Springer/TELOS, New York, 1995.

Simon Plouffe Home page ,

Steve Finch, The favorite mathematical constants

The miraculous Bailey-Borwein-Plouffe Pi Algorithm

Recognizing Numerical Constants, by David H. Bailey and Simon M. Plouffe

Organic Mathematics, at the Center for Experimental & Constructive Mathematics

N. J. A. Sloane, The On-Line Encyclopedia of Integer Sequences

The Encyclopedia of Integer Sequences and the Sequence Server

A Passion for Pi by Ivars Peterson

American Scientist , A Question of Numbers by Brian hayes, Issue of Jan-Feb 96.

Pi: A 2000-Year Search Changes Direction, Stan Wagon and Victor Adamchik,

Science News.

Plouffe constant, arctan(1/2)/Pi,

Addition Theorems and Binary expansion, by Jon Borwein and Roland Girgensohn.

[Mail a Message] HOME