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============ ============================================================================== Pi-references ------------- 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 ==============================================================================