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Skip-Term Summation of Sequences


Author: Irwin Roman
Journal: Math. Comp. 13 (1959), 117-121
DOI: https://doi.org/10.1090/S0025-5718-59-99263-4
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References | Additional Information

References [Enhancements On Off] (What's this?)

  • [1] H. T. Davis, Tables of the Higher Mathematical Functions, Principia Press, Bloomington, Indiana, 1955, p. 200-201 and 251-255.
  • [2] A. de Morgan, Differential and Integral Calculus, Baldwin and Cradock, London, 1836, p. 317-318.
  • [3] L. Euler, ``Inventio summae cuiusque serii ex dato termino generali,'' Commentarii Academiae Scientiarum Imperialis Petropolitanae, Akademiia nauk SSSR, Leningrad, v. 8, 1736, p. 9-22.
  • [4] R. B. Horgan, ``Tables of coefficients for the partial summation of series,'' MTAC, v. X, 1956, p. 156-162. MR 0084202 (18:829a)
  • [5] L. B. W. Jolley, Summation of Series, Chapman and Hall, London, 1925, p. 6.
  • [6] J. W. Lubbock, ``On the comparison of various tables of annuities,'' Camb. Phil, Soc. Trans., v. 3, 1830, p. 321-341.
  • [7] C. MacLaurin, ``A treatise of fluxions,'' T. W. & T. Ruddimans, Edinburgh, 1742, p. 673.
  • [8] Mathematical Tables Project, Tables of Lagrangian Interpolation Coefficients, Columbia University Press, New York, 1944.
  • [9] I. Roman, ``An Euler summation formula,'' Am. Math. Monthly, v. 43, 1936, p. 9-21. MR 1523550
  • [10] H. E. Salzer, ``A simple method for summing certain slowly convergent series,'' J. Math and Phys., v. 33, 1954, p. 356-359. MR 0068315 (16:863d)
  • [11] H. E. Salzer, ``Formulas for the partial summation of series,'' MTAC, v. X, 1956, p. 149-156. MR 0081528 (18:416a)
  • [12] T. B. Sprague, ``On Lubbock's formula for approximating to the value of a life annuity,'' J. Inst. Actuaries, London, v. 18, 1874, p. 305-317.
  • [13] J. F. Steffensen, Interpolation, Williams & Wilkins, Baltimore, Maryland, 1927, p. 138-148.
  • [14] E. T. Whittaker, & G. Robinson, The Calculus of Observations, Blackie, London, 1924, p. 149-150.


Additional Information

DOI: https://doi.org/10.1090/S0025-5718-59-99263-4
Article copyright: © Copyright 1959 American Mathematical Society

American Mathematical Society