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Journal: Math. Comp. 1 (1943), 45-56
DOI: https://doi.org/10.1090/S0025-5718-43-99135-5
Corrigendum: Math. Comp. 2 (1946), 63-64.
Corrigendum: Math. Comp. 1 (1943), 132.
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  • [1] A. A. Markov, O Nekotorykh Prilozheniiakh Algebraicheskikh Nepreryvnykh Drobei. [On some Applications of Algebraic Continued Fractions], Doctoral diss., St. Petersburg, 1884, p. 68; A. A. Markov, ``Sur la méthode de Gauss pour le calcul approche des intégrales,'' Math. Annalen, v. 25, 1885, p. 429; and P. Mansion, ``Détermination du reste dans la formule de quadrature de Gauss,'' Acad. Royale d. Sci. d. Lettres. et d. Beaux-Arts de Belgique, Bulletins, s. 3, v. 11, 1886, p. 303. Also in A. A. Markov, Differenzenrechnung, Leipzig, 1896, p. 68; Gauss's numerical results are given on p. 70.
  • [2] These values up to $ {U_7}$ were given by Gauss, Werke, v. 3, p. 193-195.
  • [3] J. V. Uspensky, On an expansion of the remainder in the Gaussian quadrature formula, Bull. Amer. Math. Soc. 40 (1934), no. 12, 871–876. MR 1562991, https://doi.org/10.1090/S0002-9904-1934-05990-1
  • 1. Among references to topics in paper (i) are the following: L. M. Milne-Thomson, The Calculus of Finite Differences, London, Macmillan, 1933. Chap. 7, p. 157-159; H. T. Davis, Table of the Higher Mathematical Functions, Bloomington, Ind., v. 1, 1933, p. 73-77; E.T. Whittaker and G. Robinson, The Calculus of Observations, A Treatise on Numerical Mathematics, 3d ed. London, Blackie, 1940, p. 62-65. The references in paper (ii) are to K. N. Bradfield and R. V. Southwell, ``Relaxation methods applied to engineering problems. I--the deflexion of beams under transverse loading.'' R. So. London, Proc., v. 161A, 1937, p. 155-181; L. J. Comrie, Interpolation and Allied Tables, London, H. M. Stationery Office, 1936. (Reprinted from the Nautical Almanac for 1937.), D. C. Fraser, ``On the graphic delineation of interpolation formulae,'' Inst. Actuaries. Jn., v. 43, 1909, p. 235-241; J. F. Steffensen, Interpolation, Baltimore, Williams & Wilkins, 1927.
  • [1] J. Stirling, Methodus Differentialis, London, 1730, p. 137; second ed., 1764, p. 137; English edition by F. Holliday, 1749, p. 121. A. de Moivre, Approximatio ad Summam Terminorum Binomii $ {(a + b)^n}$ in Seriem expansi, London, 1733; rev. transl. in A. de Moivre, Doctrine of Chances, London, second ed., 1738, p. 235-242; third ed., 1756, p. 243-250; for a facsimile of the 1733 publication see R. C. Archibald, ``A rare pamphlet of Moivre and some of his discoveries,'' Isis, v. 8, 1926, p. 677-683. See also C. Tweedie, James Stirling . . . , Oxford, 1922, p. 119, 203-205.


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DOI: https://doi.org/10.1090/S0025-5718-43-99135-5
Article copyright: © Copyright 1943 American Mathematical Society