From: jk87377@cc.tut.fi (Juhana Kouhia)
Newsgroups: sci.math
Subject: Pi references (Re: How is pi calculated?)
Date: 5 May 92 12:00:50 GMT
Hi,
Here is the latest list for pi-references, dated May 5, 1992.
Thank for the people who sent me references or gave information
for articles.
Here are latest additions as they are sent to me by J.M. Borwein
(others suggested the same articles).
Now I have a question: please check which reference format is more
better: the format used in Borwein's additions list or in the complete
list below?
Juhana Kouhia
====Additions follows===========
Recent papers relating to Pi:
1. J.M. Borwein and P.B. Borwein, "A cubic counterpart of Jacobi's
identity and the AGM," Trans. Amer. Math. Soc., 323(1991),691-701.
-contains three of the fastest known iterations for Pi.
2. J.M. Borwein, P.B. Borwein, and K. Dilcher, "Euler numbers,
asymptotic expansions and pi," MAA Monthly, 96(1989),681-687.
-relates Gregory's series and Pi and Euler numbers.
3. J.M. Borwein and P.B. Borwein, "An explicit cubic iteration for 9,"
BIT, 26(1986),123-126.
4. J.M. Borwein, P.B. Borwein, and D. A. Bailey, "Ramanujan, modular
equations and pi or how to compute a billion digits of pi," MAA
Monthly, 96(1989),201-219.
5. J.M. Borwein and P.B. Borwein, "Approximating pi with Ramanujan's
solvable modular equations," Proceedings of the 1986 Edmonton
conference on Constructive Function Theory, Rocky Mountain J. ,
19(1989),93-102.
-gives the algebraically most surprising iterations for Pi.
6. J.M. Borwein and P.B. Borwein, "More Ramanujan-type series for
1/pi," pp 359-374 in Ramanujan Revisited [Proceedings of the 1987
Illinois Ramanujan Centenary Conference], Academic Press(1988).
-includes the series the Chudnovskys used in their record
computation and many others of a similar ilk.
In press:
7. J.M. Borwein and I.J. Zucker, "Elliptic integral evaluation of
the Gamma function at rational values of small denominator," IMA
J. of Numer Analysis, xx(1992).
-includes agm based iterations for Gamma(n/24):
since Gamma(1/2)=Pi^(1/2) this is closely related.
8. J.M. Borwein and P.B. Borwein, "Class number three Ramanujan type
series for 1/pi," Journal of Computational and Applied Math (Special
Issue), xx(1992).
====End of additions============
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Pi-references
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Compiled by Juhana Kouhia, jk87377@cs.tut.fi
Last update May 5, 1992
Please send updates to Juhana Kouhia
Comments starting with '-' are written by J.M. Borwein.
------------------------------------------------------------------------------
David H. Bailey
The computation of pi to 29,360,000 decimal digits using Borwein'
quartically convergent algorithm
Mathematics of Computation, Vol. 50, No. 181, Jan 1988, pp. 283-296
David H. Bailey
Numerical results on the transcendence of constants involving pi,
e, and Euler's constant
Mathematics of Computation, Vol. 50, No. 181, Jan 1988, pp. 275-281
P. Beckmann
A history of pi
Golem Press, CO, 1971 (fourth edition 1977)
J.M. Borwein and P.B. Borwein
The arithmetic-geometric mean and fast computation of elementary
functions
SIAM Review, Vol. 26, 1984, pp. 351-366
J.M. Borwein and P.B. Borwein
More quadratically converging algorithms for pi
Mathematics of Computation, Vol. 46, 1986, pp. 247-253
J.M. Borwein and P.B. Borwein
An explicit cubic iteration for 9
BIT, Vol. 26, 1986, pp. 123-126
J.M. Borwein and P.B. Borwein
Pi and the AGM. A Study in Analytic Number Theory and Computational Complexity
John Wiley & Sons. New York, 1987
J.M. Borwein and P.B. Borwein
More Ramanujan-type series for 1/pi
pp. 359-374 in Ramanujan Revisited [Proceedings of the 1987
Illinois Ramanujan Centenary Conference], Academic Press(1988)
-includes the series the Chudnovskys used in their record
computation and many others of a similar ilk
J.M. Borwein and P.B. Borwein
Ramanujan and pi
Scientific American, Feb 1988, pp. 112-117
J.M. Borwein, P.B. Borwein, and K. Dilcher
Euler numbers, asymptotic expansions and pi
MAA Monthly, Vol. 96, 1989, pp. 681-687
-relates Gregory's series and Pi and Euler numbers
J.M. Borwein, P.B. Borwein, and D. A. Bailey
Ramanujan, modular equations and pi or how to compute a billion digits
of pi
MAA Monthly, Vol. 96, 1989, pp. 201-219
J.M. Borwein and P.B. Borwein
Approximating pi with Ramanujan's solvable modular equations
Proceedings of the 1986 Edmonton conference on Constructive Function
Theory, Rocky Mountain J., Vol. 19, 1989, pp. 93-102
-gives the algebraically most surprising iterations for Pi
J.M. Borwein and P.B. Borwein
A cubic counterpart of Jacobi's identity and the AGM
Trans. Amer. Math. Soc., Vol. 323, 1991, pp. 691-701
-contains three of the fastest known iterations for Pi
J.M. Borwein and P.B. Borwein
Class number three Ramanujan type series for 1/pi
Journal of Computational and Applied Math (Special Issue), xx(1992)
J.M. Borwein and I.J. Zucker
Elliptic integral evaluation of the Gamma function at rational values
of small denominator
IMA J. of Numer Analysis, xx(1992)
-includes agm based iterations for Gamma(n/24): since
Gamma(1/2)=Pi^(1/2) this is closely related
Shlomo Breuer and Gideon Zwas
Mathematical-educational aspects of the computation of pi
Int. J. Math. Educ. Sci. Technol., Vol. 15, No. 2, 1984, pp. 231-244
Harley Flanders
Algorithm of the bi-month: Computing pi
College Mathematics Journal, Vol. 18, 1987, pp. 230-235
Y. Kanada and Y. Tamura
Calculation of pi to 10,013,395 decimal places based on the
Gauss-Legendre algorithm and Gauss arctangent relation
Computer Centre, University of Tokyo, 1983
R. Lynch and H.A. Mavromatis
N-dimensional harmonic oscillator yields monotonic series for the
mathematical constant pi
Journal of Computational and Applied Mathematics, Vol. 30, No. 2,
May 1990, pp. 127-137
H.A. Mavromatis
Two doubly infinite sets of series for pi
Journal of Approximation Theory, Vol. 60, 1990, pp. 1-10
N.D. Mermin
Pi in the sky
Letter to the Editor
American Journal of Physics, Vol. 55, 1987, p. 584
D.J. Newman
A simplified version of the fast algorithms of Brent and Salamin
Mathematics of Computation, Vol. 44, No. 169, Jan 1985, pp. 207-210
Morris Newman and Daniel Shanks
On a sequence arising in series for pi
Mathematics of computation, Vol. 42, No. 165, Jan 1984, pp. 199-217
E. Salamin
Computation of pi using arithmetic-geometric mean
Mathematics of Computation, Vol. 30, 1976, pp. 565-570
D. Shanks and J.W. Wrench, Jr.
Calculation of pi to 100,000 decimals
Mathematics of Computation, Vol. 16, 1962, pp. 76-99
Daniel Shanks
Dihedral quartic approximations and series for pi
J. Number Theory, Vol. 14, 1982, pp.397-423
David Singmaster
The legal values of pi
The Mathematical Intelligencer, Vol. 7, No. 2, 1985
John Todd
A very large slice of pi
Review for the book "Pi and the AGM. A study in analytic number theory
and computational complexity" by J.M. Borwein and P.B. Borwein
The Mathematical Intelligencer, Vol. 11, No. 3, 1989, pp. 73-77
Stan Wagon
Is pi normal?
The Mathematical Intelligencer, Vol. 7, No. 3, 1985, pp. 65-67
J.W. Wrench, Jr.
The evolution of extended decimal approximations to pi
The Mathematics Teacher, Vol. 53, 1960, pp. 644-650
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