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Recent Mathematical Tables


Journal: Math. Comp. 5 (1951), 133-160
DOI: https://doi.org/10.1090/S0025-5718-51-99428-8
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  • [1] K. Inkeri, ``Über den Euklidischen Algorithmus in quadratischen Zahlkörpern,'' Acad. Sci. Fennicae, Annales, v. 41, 1947, p. 5-34. MR 0025498 (10:15g)
  • [1] H. Bergström, ``Die Klassenzahlformel für reelle quadratische Zahlkörper mit zusammengesetzter Diskriminante als Produkt verallgemeinterter Gaussscher Summen,'' Jn. reine angew. Math., v. 186, 1944, p. 91-115. MR 0013402 (7:148b)
  • [1] Not only the publications of Goodwyn to which we refer, but others, have been discussed in thorough fashion by J. W. L. Glaisher: (i) Report of the Comm. on Mathematical Tables, 1873, p. 31-33, 150; (ii) ``On circulating decimals with special reference to Henry Goodwyn's 'Table of circles' and 'Tabular series of decimal quotients' (London 1818-1823),'' Cambridge Phil. Soc., Proc., v. 3, 1878, p. 185-206; (iii) ``On a property of vulgar fractions,'' Phil. Mag., s. 5, v. 7, 1879, p. 321-336. We have already quoted DeMorgan's Statement of 1861 [MTAC, v. 2, p. 87] concerning Goodwyn: ``His manuscripts, an enormous mass of similar calculations, came into the possession of Dr. Olinthus Gregory, and were purchased by the Royal Society at the sale of his [Gregory's] books in 1842.'' In the above publications of Glaisher it is stated that no trace of the papers could be found at the Royal Society. Neville's statement, p. xi, ``Goodwyn left a mass of papers, no one knows what became of them,'' is therefore slightly misleading.
  • [1] K. G. J. Jacobi, ``Über die Kreistheilung und ihre Anwendung auf die Zahlentheorie,'' Jn. reine angew. Math., v. 30, 1846, p. 166-182.
  • [2] K. G. Reuschle, Mathematische Abhandlung, enthaltend: Neue Zahlentheoretische Tabellen, Stuttgart, 1856.
  • [3] A. J. C. Cunningham, Quadratic Partitions. London, 1904; Quadratic and Linear Tables. London, 1927.
  • [4] B. van der Pol, Verslagen van de Maatschappij Diligentia, The Hague, 1946. A copy of this diagram woven in red and white squares hangs on the wall of the reviewer's study, a gift from the author.
  • [1] The curve $ t = {x^t}$ has been frequently studied before. For example: (a) J. F. C. Hessel, ``Über das merkwürdige Beispiel einer zum Theil punctirt gebildeten Curve das der Gleichung entspricht $ y = \sqrt[x]{x}$,'' Archiv Math. Phys., v. 14, 1850, p. 169-187; H. Scheffer, ``Über die durch die Gleichung $ y = \sqrt[x]{x}$ dargestellten Curven,'' Archiv Math. Phys., v. 16, 1851, p. 133-137. The role which $ \xi = {\omega ^\xi }$ plays in Cantor's theory of transfinite numbers will be recalled; see, for example, G. Cantor, Math. Annalen, v. 49, 1897, p. 242-246 (also the English translation of P. E. B. Jourdain, Open Court, 1915, p. 195-201).
  • [1] H. E. Salzer, ``Formulas for direct and inverse interpolation of a complex function tabulated along equidistant circular arcs,'' Jn. Math. Physics, v. 24, 1945, p. 141-143, MTAC, v. 2, p. 73, and ``Alternative formulas for direct interpolation of a complex function tabulated along equidistant circular arcs,'' Jn. Math. Physics, v. 26, 1947, p. 56-61. MR 0020340 (8:535a)
  • [1] R. A. Fisher & F. Yates, Statistical Tables for Biological, Agricultural, and Medical Research. London, 1948. MR 0030288 (10:740c)
  • [1] P. L. Chebyshev, ``Sur l'interpolation par la méthode des moindres carrés,'' Akad. Nauk, Leningrad, Mémoires, s. 7, v. 1, no. 15, 1859, p. 1-24. Oeuvres, v. 1, p. 471-498.
  • [2] R. A. Fisher & F. Yates, Statistical Tables for Biological, Agricultural and Medical Research. Third ed., London, 1948. (First ed., 1938.) MR 0030288 (10:740c)
  • [3] R. L. Anderson & E. E. Houseman, Tables of Orthogonal Polynomial Values Extended to $ N = 104$. Ames, Iowa, Iowa State College of Agriculture and Mechanic Arts, 1942. (Research Bulletin 297, p. 593-672, Agricultural Experiment Station, Statistical Sections.) [MTAC, v. 1, p. 148-150, v. 5, p. 81.] MR 0009153 (5:110e)
  • [4] D. van der Reyden, ``Curve fitting by the orthogonal polynomials of least squares,'' Onderstepoort Journal of Veterinary Science and Animal Industry, v. 28, 1943, p. 355-404.
  • [5] Raymond T. Birge, ``Least-squares' fitting of data by means of polynomials,'' Review of Modern Physics, v. 19, 1947, p. 298-347. MR 0024683 (9:534e)
  • [6] J. W. Weinberg, ``Mathematical appendix,'' ibid., p. 348-360.
  • [7] Lila F. Knudsen, ``A punched card technique to obtain coefficients of orthogonal polynomials,'' Am. Stat. Assn., Jn., v. 37, 1942, p. 496-506. MR 0007132 (4:92a)
  • [1] M. S. Bartlett, ``Properties of sufficiency and statistical tests,'' R. Soc. London, Proc., v. 160A, 1937, p. 268-282.
  • [2] E. S. Pearson & H. O. Hartley, ``The probability integral of the range in samples of $ n$ observations from a normal population,'' Biometrika, v. 32, 1942, p. 301-310. MR 0006641 (4:19c)
  • [1] Karl Pearson, Tables of the Incomplete $ \Gamma $-Function. London, 1922.
  • [2] E. C. Molina, Poisson's Exponential Binomial Limit. New York, 1945.
  • [3] L. R. Salvosa, ``Tables of Pearson's type III function,'' Annals Math. Stat., v. 1, 1930, p. 191-198. Appendix, p. 1-187.
  • [4] H. T. Davis & W. F. C. Nelson, Elements of Statistics with Applications to Economic Data. Bloomington, Ind., 1935.
  • [1] H. J. Godwin, ``Some low moments of order statistics,'' Annals Math. Stat., v. 20, 1949, p. 279-285. [See MTAC, v. 4, p. 20.] MR 0030162 (10:722f)
  • [1] J. Neyman & B. Tokarska, ``Errors of the second kind in testing 'Student's' hypothesis,'' Am. Stat. Assn. Jn., v. 31, 1936, p. 318-326.
  • [1] E. Lord, ``The use of range in place of standard deviation in the $ t$-test,'' Biometrika, v. 34, 1947, p. 41-67; ``Power of the modified $ t$-test ($ u$-test) based on the range,'' Biometrika, v. 37, 1950, p. 64-77. [RMT 897]
  • [1] E. L. Grant, Statistical Quality Control. New York, 1946.
  • [1] H. B. Mann & A. Wald, ``On the choice of the number of class intervals in the application of the chi-square test,'' Annals Math. Stat., v. 13, 1942, p. 306-317. MR 0007224 (4:105a)
  • [1] B. Pal, ``On the numerical calculation of the roots of the equations $ P_n^m(\mu ) = 0$ and $ \tfrac{d}{{d\mu }}P_n^m(\mu ) = 0$ regarded as equations in $ n$,'' Calcutta Math. Soc., Bull., v. 9, 1918, p. 85-95 and v. 10, 1919, p. 187-194.
  • [1] R. Grammel, ``Eine Verallgemeinerung der Kreis- und Hyperbelfunktionen.'' Ing.-Arch., v. 16, 1948, p. 188-200. MR 0025631 (10:38c)
  • [1] A. Walther, ``Anschauliches zur Gibbsschen Erscheinung und zur Annäherung durch arithmetische Mittel,'' Math. Zeit., v. 42, 1937, p. 355-364. MR 1545681
  • [1] NBSCL, Table of the Bessel Functions $ {J_0}(z)$ and $ {J_1}(z)$ for Complex Arguments. 2nd ed., New York, 1947 [MTAC, v. 3, p. 25].
  • [1] J. McDougall & E. C. Stoner, ``The computation of Fermi-Dirac functions,'' R. Soc. London, Phil. Trans., v. 237A, 1938, p. 67-104. C. Truesdell, ``On a function which occurs in the theory of the structure of polymers,'' Annals Math., s. 2, v. 46, 1945, p. 150 [MTAC, v. 1, p. 445].


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DOI: https://doi.org/10.1090/S0025-5718-51-99428-8
Article copyright: © Copyright 1951 American Mathematical Society

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