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Evaluation at half periods of Weierstrass' elliptic function with rhombic primitive period-parallelogram


Authors: Chih Bing Ling and Chen-Peng Tsai
Journal: Math. Comp. 18 (1964), 433-440
MSC: Primary 65.25
DOI: https://doi.org/10.1090/S0025-5718-1964-0165661-X
MathSciNet review: 0165661
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  • [1] Chih Bing Ling, Evaluation at half periods of Weierstrass’ elliptic function with rectangular primitive period parallelogram, Math. Comput. 14 (1960), 67–70. MR 0110179, https://doi.org/10.1090/S0025-5718-1960-0110179-X
  • [2] E. T. Copson, Theory of Functions of a Complex Variable, Oxford University Press, New York, 1935, p. 359-362.
  • [3] A. Erdelyi, et al., Higher Transcendental Functions, Vol. 2, McGraw-Hill, New York, 1953, p. 328-361. In the formulas (8) and (9) on p. 355, the summation should each begin with n = 1 instead of n = 0.
  • [4] J. W. L. Glaisher, ``Tables of $ 1 \pm {2^{ - n}} + {3^{ - n}} \pm {4^{ - n}} + $ etc. and $ 1 + {3^{ - n}} + {5^{ - n}} + {7^{ - n}} + $ etc. to 32 places of decimals,'' Quart. J. Pure Appl. Math., v. 45, 1914, p. 141-158.
  • [5] Circular and Hyperbolic Functions. Exponential and Sine and Cosine Integrals. Factorial Function and Allied Functions. Hermitian Probability Functions, 2nd ed., Mathematical Tables, Volume 1, Cambridge, at the University Press; New York, The Macmillan Company, 1946. MR 0014819
  • [6] C. E. Van Orstrand, ``Tables of the exponential function and of the circular sine and cosine to radian argument,'' Memoirs of U. S. National Academy of Sciences, Vol. 14, 1925, Fifth Memoir, p. 3-79.

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DOI: https://doi.org/10.1090/S0025-5718-1964-0165661-X
Article copyright: © Copyright 1964 American Mathematical Society