References

# 7. References

[Abramowitz et al. 1964] M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions, National Bureau of Standards, Washington, D.C., 1964.

[Ahlgren et al. 2001] S. Ahlgren and K. Ono, Addition and counting: the arithmetic of partitions, Notices of the AMS 48 (2001), p. 978.

[Bailey et al. 1997] D. H. Bailey, P. B. Borwein, and S. Plouffe, On The Rapid Computation of Various Polylogarithmic Constants, Math. Comp. 66 (1997), p. 903.

[Bateman et al. 1953] Bateman and Erdelyi, Higher Transcendental Functions, McGraw-Hill, 1953.

[Beeler et al. 1972] M. Beeler, R. W. Gosper, and R. Schroeppel, Memo No. 239, MIT AI Lab (1972), now available online (the so-called "Hacker's Memo" or "HAKMEM").

[Borwein 1995] P. Borwein, An efficient algorithm for Riemann Zeta function (1995), published online and in Canadian Math. Soc. Conf. Proc., 27 (2000), pp. 29-34.

[Borwein et al. 1999] J. M. Borwein, D. M. Bradley, R. E. Crandall, Computation strategies for the Riemann Zeta function, online preprint CECM-98-118 (1999).

[Brent 1975] R. P. Brent, Multiple-precision zero-finding methods and the complexity of elementary function evaluation, in Analytic Computational Complexity, ed. by J. F. Traub, Academic Press, 1975, p. 151; also available online from Oxford Computing Laboratory, as the paper `rpb028`.

[Brent 1976] R. P. Brent, The complexity of multiple-precision arithmetic, Complexity of Computation Problem Solving, 1976; R. P. Brent, Fast multiple-precision evaluation of elementary functions, Journal of the ACM 23 (1976), p. 242.

[Brent 1978] R. P. Brent, A Fortran Multiple-Precision Arithmetic Package, ACM TOMS 4, no. 1 (1978), p. 57.

[Brent et al. 1980] R. P. Brent and E. M. McMillan, Some new algorithms for high precision computation of Euler's constant, Math. Comp. 34 (1980), p. 305.

[Crenshaw 2000] J. W. Crenshaw, MATH Toolkit for REAL-TIME Programming, CMP Media Inc., 2000.

[Damgard et al. 1993] I. B. Damgard, P. Landrock and C. Pomerance, Average Case Error Estimates for the Strong Probable Prime Test, Math. Comp. 61, (1993) pp. 177-194.

[Davenport et al. 1989] J. H. Davenport, Y. Siret, and E. Tournier, Computer Algebra, systems and algorithms for algebraic computation, Academic Press, 1989.

[Davenport 1992] J. H. Davenport, Primality testing revisited, Proc. ISSAC 1992, p. 123.

[Fee 1990] G. Fee, Computation of Catalan's constant using Ramanujan's formula, Proc. ISSAC 1990, p. 157; ACM, 1990.

[Godfrey 2001] P. Godfrey (2001) (unpublished text): http://winnie.fit.edu/~gabdo/gamma.txt .

[Gourdon et al. 2001] X. Gourdon and P. Sebah, The Euler constant; The Bernoulli numbers; The Gamma Function; The binary splitting method; and other essays, available online at http://numbers.computation.free.fr/Constants/ (2001).

[Haible et al. 1998] B. Haible and T. Papanikolaou, Fast Multiprecision Evaluation of Series of Rational Numbers, LNCS 1423 (Springer, 1998), p. 338.

[Johnson 1987] K. C. Johnson, Algorithm 650: Efficient square root implementation on the 68000, ACM TOMS 13 (1987), p. 138.

[Kanemitsu et al. 2001] S. Kanemitsu, Y. Tanigawa, and M. Yoshimoto, On the values of the Riemann zeta-function at rational arguments, The Hardy-Ramanujan Journal 24 (2001), p. 11.

[Karp et al. 1997] A. H. Karp and P. Markstein, High-precision division and square root, ACM TOMS, vol. 23 (1997), p. 561.

[Knuth 1973] D. E. Knuth, The art of computer programming, Addison-Wesley, 1973.

[Lanczos 1964] C. J. Lanczos, J. SIAM of Num. Anal. Ser. B, vol. 1, p. 86 (1964).

[Luke 1975] Y. L. Luke, Mathematical functions and their approximations, Academic Press, N. Y., 1975.

[Olver 1974] F. W. J. Olver, Asymptotics and special functions, Academic Press, 1974.

[Pollard 1978] J. Pollard, Monte Carlo methods for index computation mod p, Mathematics of Computation, vol. 32 (1978), pp. 918-924.

[Pomerance et al. 1980] Pomerance et al., Math. Comp. 35 (1980), p. 1003.

[Rabin 1980] M. O. Rabin, Probabilistic algorithm for testing primality, J. Number Theory 12 (1980), p. 128.

[Smith 1989] D. M. Smith, Efficient multiple-precision evaluation of elementary functions, Math. Comp. 52 (1989), p. 131.

[Smith 2001] D. M. Smith, Algorithm 814: Fortran 90 software for floating-point multiple precision arithmetic, Gamma and related functions, ACM TOMS 27 (2001), p. 377.

[Spouge 1994] J. L. Spouge, J. SIAM of Num. Anal. 31 (1994), p. 931.

[Sweeney 1963] D. W. Sweeney, Math. Comp. 17 (1963), p. 170.

[Thacher 1963] H. C. Thacher, Jr., Algorithm 180, Error function for large real X, Comm. ACM 6, no. 6 (1963), p. 314.

[Tsimring 1988] Sh. E. Tsimring, Handbook of special functions and definite integrals: algorithms and programs for calculators, Radio and communications (publisher), Moscow (1988) (in Russian).

[von zur Gathen et al. 1999] J. von zur Gathen and J. Gerhard, Modern Computer Algebra, Cambridge University Press, 1999.