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- Math. Comp. 1 (1943), 45-56 Request permission
Corrigendum: Math. Comp. 2 (1946), 63-64.
Corrigendum: Math. Comp. 1 (1943), 132.
References
- A. A. Markov, O Nekotorykh Prilozheniiakh Algebraicheskikh Nepreryvnykh Drobeǐ. [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.
These values up to ${U_7}$ were given by Gauss, Werke, v. 3, p. 193-195.
- 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, DOI 10.1090/S0002-9904-1934-05990-1 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. 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.
Additional Information
- © Copyright 1943 American Mathematical Society
- Journal: Math. Comp. 1 (1943), 45-56
- DOI: https://doi.org/10.1090/S0025-5718-43-99135-5