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Mathematics of Computation

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Journal: Math. Comp. 24 (1970), 475-502
DOI: https://doi.org/10.1090/S0025-5718-70-99853-4
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References [Enhancements On Off] (What's this?)

  • [1] Donald E. Knuth, The Art of Computer Programming, Vol. I: Fundamental Algorithms, AddisonWesley Publishing Co., Reading, Mass., 1968. (See Math. Comp., v. 23, 1969, pp. 447-450, RMT 18.) MR 0378456 (51:14624)
  • [1] WE. Mansell, Tables of Natural and Common Logarithms to 110 Decimals, Royal Society Mathematical Tables, Vol. 8, Cambridge Univ. Press, New York, 1964. (See Math. Comp., v. 19, 1965, p. 332, RMT 35.) MR 0166398 (29:3675)
  • [2] W. S. Aldis, "Tables for the solution of the equation $ {d^2}y/d{x^2} + (1/x)dy/dx - (1 + {n^2}/{x^2})y = 0$," Proc. Roy. Soc. London, v. 64, 1899, pp. 203-223.
  • [1] A. R. Curtis, Tables of Jacobian Elliptic Functions whose Arguments are Rational Fractions of the Quarter Period, National Physical Laboratory, Mathematical Tables, Vol. 7, Her Majesty's Stationery Office, London, 1964. (See Math. Comp., v. 19, 1965, pp. 154-155, RMT 10.) MR 0167644 (29:4916)
  • [2] H. E. Salzer, "Quick calculation of Jacobian elliptic functions," Comm. ACM, v. 5, 1962, p. 399.
  • [1] Y. L. Luke, Integrals of Bessel Functions, McGraw-Hill Book Co., New York, 1962, pp. 314-318. (See also Math. Comp., v. 17, 1963, pp. 318-320.) MR 0141801 (25:5198)
  • [1] O. P. Gupta & S. Luthra, "Partition into primes," Proc. Nat. Inst. Sci. India, v. 21, 1955, pp. 181-184. MR 0074447 (17:587b)
  • [2] M. Abramowitz & I. A. Stegun, editors, Handbook of Mathematical Functions, Dover, New York, 1965; Section 24, "Combinatorial analysis" (see 24.2.1, 24.2.2, Table 24.5).
  • [3] G. H. Hardy & S. Ramanujan, "Asymptotic formulae for the distribution of integers of various types," Proc. London Math. Soc., (2), v. 16, 1917, pp. 112-132; see Eq. (5.281).
  • [1] UMT 29, Math. Comp., v. 23, 1969, p. 458. MR 0238502 (38:6778)
  • [2] UMT 50, Math. Comp., v. 23, 1969, p. 683.
  • [3] D. H. Lehmer et al., "Integer sequences having prescribed quadratic character," Math. Comp., v. 24, 1970, pp. 433-451. MR 0271006 (42:5889)
  • [1] S. Ramanujan, "On certain arithmetical functions," Trans. Cambridge Philos. Soc., v. 22, 1916, pp. 159-184; see especially §§ 16-18. A short table of $ \tau (n)$ for $ n = 1(1)30$ is given here.
  • [2] G. N. Watson, "A table of Ramanujan's function $ \tau (n)$," Proc. London Math. Soc., (2), v. 51, 1950 (paper is dated 1942), pp. 1-13. MR 0028887 (10:514c)
  • [3] D. H. Lehmer, Tables of Ramanujan $ \tau (n)$, UMT 101, MTAC, v. 4, 1950, p. 162.
  • [4] Margaret Ashworth & A. O. L. Atkin, Tables of $ {p_k}(n)$, UMT 1, Math. Comp., v. 21, 1967, p. 116. MR 0223091 (36:6140)
  • [5] G. H. Hardy, Ramanujan, Chelsea reprint, New York, 1959, Chapter X and §§9.17, 9.18.
  • [1] D. H. Lehmer, Guide to Tables in the Theory of Numbers, Bulletin No. 105, National Research Council, Washington, D. C., 1941, p. 73. MR 0003625 (2:247a)


Additional Information

DOI: https://doi.org/10.1090/S0025-5718-70-99853-4
Article copyright: © Copyright 1970 American Mathematical Society

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