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- Math. Comp. 2 (1947), 249-276 Request permission
Corrigendum: Math. Comp. 2 (1947), 320.
References
- E. Lebon, Table de Caractéristiques de Base 30 030 donnant, en un seul Coup d’Oeil, les Facteurs Premiers des Nombres Premiers avec 30 030 et Inférieurs à 901 800 900, v. 1, pt. 1, Paris, 1920.
A. J. C. Cunningham, Binomial Factorisations, v. 1, London, 1923, p. 113-119.
M. Kraitchik, Recherches sur la Théorie des Nombres, v. 2, Paris, 1929, p. 116-117.
N. G. W. H. Beeger, Additions and Corrections to Binomial Factorisations by Cunningham. Amsterdam, 1933, 1945.
See MTAC, v. 1, p. 6; v. 2, p. 71-2, 210-211.
See MTAC, v. 2, p. 211.
C. F. Degen, Canon Pellianus . . ., Copenhagen, 1817.
A. Cayley, “Report of a committee appointed for the purpose of carrying on the tables connected with the Pellian equation from the point where the work was left by Degen in 1817,” BAAS, Report, 1893, p. 73-120; also Collected Mathematical Papers, v. 13, 1897, p. 430-467. [These tables were computed by C. E. Bickmore.]
E. E. Whitford, The Pell Equation, New York, 1912, p. 164-190.
- Freiherrn Max von Thielmann, Zur Pellschen Gleichung, Math. Ann. 95 (1926), no. 1, 635–640 (German). MR 1512297, DOI 10.1007/BF01206630
- Derrick Henry Lehmer, Guide to Tables in the Theory of Numbers, National Research Council, Washington, D.C., 1941. Bulletin of the National Research Council, No. 105. MR 0003625 C. A. Roberts, “Table of the square roots of the prime numbers of the form $4m + 1$ less than 10000 expanded as periodic continued fractions,” Math. Magazine, v. 2, p. 105-120, 1892. G. Wertheim, Aufgangsgründe der Zahlenlehre. Brunswick, 1902, p. 412-417. J. V. Uspensky & M. A. Heaslet, Elementary Number Theory. New York and London, 1939, p. 477-480.
- H. O. Hartley, Testing the homogeneity of a set of variances, Biometrika 31 (1940), 249–255. MR 2071, DOI 10.1093/biomet/31.3-4.249 M. S. Bartlett, “Properties of sufficiency and statistical tests,” R. Soc. London, Proc., v. 160A, 1937, p. 268-282. J. Neyman & E. S. Pearson, “On the problem of $k$ samples,” Akad. umiejetności, Bull. Intern., 1931A, p. 460-481. D. T. Bishop & U. S. Nair, “A note on certain methods of testing for the homogeneity of a set of estimated variance,” R. Statist. Soc., Jn., v. 102, Suppl. v. 6, 1939, p. 89-99. B. Sieger, “Die Beugung einer ebenen elektrischen Welle an einem Schirm von elliptischem Querschnitt,” Ann. d. Phys., s. 4, v. 27, 1908, p. 626-664. M. J. O. Strutt, Lamésche-Mathieusche und verwandte Funktionen der Physik u. Technik, (Ergebnisse d. Math., v. 1, no. 3), Berlin, 1932, p. 46-48. See MTAC, v. 1, p. 361, 425; and v. 2, p. 31 [where ${L_n}(x)$ is defined without the factor ${(n!)^{ - 1}}$], 89. J. L. Lagrange, “Solution de différents problèmes de calcul intégral,” Miscellanea Taurinensia, v. 3, 1762-65; Oeuvres, v. 1, Paris, 1867, “Des oscillations d’un fil fixe par une de ses extrémités, et chargé d’un nombre quelconque de poids,” p. 534-536; there are four of the polynomials on p. 536. N. H. Abel, Oeuvres Complètes, Christiania, 1881, v. 2, p. 284. E. Schrödinger, Annalen d. Physik, v. 385, 1926, p. 485. Pinney, Jn. Math. Phys., v. 25, 1946, p. 49f. Harry Bateman’s Bibliography, p. 77-79. G. N. Watson, A Treatise on the Theory of Bessel Functions, p. 328-329; tables, p. 666-697. J. R. Airey, BAAS, Report, 1924, p. 280f, - $- {H_{ - 1}}(x)$ is also tabulated here for the same range. Jahnke & Emde, Tables of Functions, fourth ed., New York, 1945, p. 219f. ${H_0}(x)$ is also tabulated here for the same range, p. 212f, and 218f. There are also two other tables of ${H_0}(x)$ and ${H_1}(x)$, to 4D, by S. P. Glazenap, Matematicheskie i Astronomicheskie Tablitsy, Leningrad, 1932, p. 110f, $x = 0(.02)16$, an abridgment of Watson; and by N. W. McLachlan, Bessel Functions for Engineers, 1934, p. 176, $x = 0(.1)15.9$. See MTAC, v. 1, p. 305. P. Siemon, Ueber die Integrale einer nicht homogenen Differentialgleichung zweiter Ordnung. Progr. Luisenschule. Berlin, 1890; see Jahrb. Fort. d. Math., 1890, p. 340f. J. Walker, The Analytical Theory of Light, Cambridge, 1904, p. 392f. S. P. Owen, “Table of values of the integral $\int _0^x {{K_0}(t)dt}$,” Phil. Mag., s. 6, v. 47, 1924, p. 736; see also MTAC, v. 1, p. 245, 247, 301. See also N. W. McLachlan & A. L. Meyers, (a) “The ster and stei functions” (b) “Integrals involving Bessel and Struve functions,” Phil. Mag., s. 7, v. 21, 1936, p. 425-436, 437-448.
- W. C. Hahn, A new method for the calculation of cavity resonators, J. Appl. Phys. 12 (1941), 62–68. MR 4183, DOI 10.1063/1.1712853 O. Schlömilch, “Ueber Facultätreihen,” Z. Math. u. Phys., v. 4, 1859, p. 390f. K. Schwarzschild, (a) “Ueber das Gleichgewicht der Sonnenatmosphäre,” Gesell, d. Wissen., Göttingen, Nach., Math-phys. Kl., 1906: p. 41f; (b) “Über Diffusion und Absorption in der Sonnenatmosphäre,” Akad. d. Wissen., Berlin, Sitzb., 1914, p. 1183f. A. S. Eddington, The Internal Constitution of the Stars, Cambridge, 1926, p. 333. E. Hopf, Mathematical Problems of Radiative Equilibrium (Cambridge Tracts . . ., no. 31), 1934, p. 21, etc.
- A. Majid Mian and S. Chapman, Approximate formulae for functions expressed as definite integrals, Philos. Mag. (7) 33 (1942), 115–130. MR 6237, DOI 10.1080/14786444208521354
Additional Information
- © Copyright 1947 American Mathematical Society
- Journal: Math. Comp. 2 (1947), 249-276
- DOI: https://doi.org/10.1090/S0025-5718-47-99590-2