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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

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The 2020 MCQ for Mathematics of Computation is 1.78.

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Math. Comp. 1 (1944), 142-160 Request permission
References
    P. L. Chebyshev, “Sur les fractions continues,” Jn. d. Math., s. 2, v. 3, 1858, p. 289-323. Oeuvres, St. Petersburg, v. 1, 1899, p. 201-230. Chebyshev, “Sur l’interpolation par la mĂ©thode des moindres carrĂ©s,” Akad. Nauk, Leningrad, MĂ©moires, s. 7, v. 1, 1859, p. 1-24. Oeuvres, v. 1, p. 471-498. G. Szegö, Orthogonal Polynomials, Am. Math. So., Coll. Publ., v. 22, New York, 1939. F. Esscher, “Ueber die Sterblichkeit in Schweden, 1866-1914,” Lund, Observatoriet, Meddel., s. 2, v. 23, 1920, p. 10-21. Ch. Jordan, “Sur une sĂ©rie de polynomes dont chaque somme partielle rĂ©presente la meilleure approximation d’un degrĂ© donnĂ© suivant la mĂ©thode des moindres carrĂ©s,” London Math. So., Proc., s. 2, v. 20, 1920, p. 297-325. R. A. Fisher, “Studies in Crop Variation.—I. An examination of the yield of dressed grain from Broadbalk,” Jn. Agric. Sci., v. 11, 1921, p. 107-135. R. A. Fisher, Statistical Methods for Research Workers, Edinburgh, third ed., 1930. F. E. Allan, “The general form of the orthogonal polynomials for simple series, with proofs of their simple properties,” R. So. Edinburgh, Proc., v. 50, 1930, p. 310-320. Chebyshev, “Sur l’interpolation,” Akad. Nauk, Zapiski, v. 4, 1864. Oeuvres, v. 1, p. 539-560. A. C. Aitken, “On the graduation of data by the orthogonal polynomials of least squares,” R. So. Edinburgh, Proc., v. 53, 1933, p. 54-78. W. Hahn, “Bericht ĂŒber die Nullstellen der Laguerreschen und der Hermiteschen Polynome,” Deutsche Mathem.-Ver., Jahresb., v. 44, 1934, p. 215-236. It is here pointed out, following Hermite, that the ${H_n}(x)$ first occurred in 1836 in a paper of Sturm, and that in 1839 they are incidentally mentioned in a paper by Chebyshev. B. Russell (Jn. Math. Phys., M.I.T., v. 12, 1933, p. 291-297) has defined a Hermite function by the relation ${\phi _n}(x) = {2^n}{e^{ - \tfrac {1}{2}{x^2}}}{H_n}(x)$ and given a table of ${\phi _n}(x)$ for $n = 0(1)11$, and $x = [0.00(0.04)1.00(0.10)4.00(0.20)7.00,7.50,8.00;{\text {to at least 5S]}}$. M. Koppe, Die Ausbreitung einer ErschĂŒtterung an der Wellenmaschine durch einen neuen Grenzfall der Besseischen Functionen, Progr. Andreas Realgymn., Berlin, 1899; see also Forts. Math., v. 30, p. 420-421. W. Mc. F. Orr, “Note on the radiation from an alternating circular electric current,” Phil. Mag., s. 6, v. 7, 1904, p. 336-341. F. Pollaczek, “Uber die Fortpflanzung mechanischer VorgĂ€nge in einem linearen Gitter,” Annalen d. Physik, s. 5, v. 2, 1929, p. 991-1011. T. H. Havelock, “Studies in wave resistance: the effect of parallel middle body,” R. So. London, Proc., v. 108 A, 1925, p. 77-92; “Ship waves: their variation with certain systematic changes of form,” R. So. London, Proc., v. 136 A, 1932, p. 465-471. G. N. Watson, Theory of Bessel Functions, Cambridge, Univ. Press, 1922, p. 752. S. P. Glazenap, Matematicheskie i Astronomicheskie Tablitsy, Leningrad, Acad. Sci., 1932, p. 97. P. Debye, “Zerstreuung von Röntgenstrahlen,” Annalen d. Physik, s. 4, v. 46, 1915, p. 809-823. F. A. Fischer, “Über die akustische Strahlungsleistung von Strahlengruppen insbesondere der Kreis- und Kugelgruppen,” Elek. Nach. Tech., v. 9, 1932, p. 147-155. M. Blackman, “On the intensities of electron diffraction rings,” R. So. London, Proc., v. 173A, 1939, p. 68-82. H. Buchholz, “Die Wechselstromausbreitung im Erdreich unterhalb einer einseitig offenen und unendlich langen vertikalen Leiterschleife im Luftraum,” Archiv f. Elektrotechnik, v. 30, 1936, p. 1-33. E. Lommel, “Über eine mit den Bessel’schen Funktionen verwandte Funktion,” Math. Ann., v. 9, 1876, p. 425-444. O. J. Lodge and A. Lodge, “The rotation of the plane of polarization of light by the discharge of a Leyden jar,” Phil. Mag., s. 5, v. 27, 1889, p. 339-346. M. Lerch [Speculations on some questions in integral equations] (Bohemian), ČeskĂĄ Akad., Rozpravy, Class II, v. 5, 1896, No. 23, 16 p.; Forts. Math., v. 27, 1896, p. 233-235. B. van der Pol, “On the operational solution of linear differential equations and an investigation of the properties of these solutions,” Phil. Mag., s. 7, v. 8, 1929, p. 861-898. P. Humbert, “Sur les fonctions de Bessel-intĂ©grales,” Inst. d. France Acad. d. Sci., Comptes Rendus, v. 195, 1932, p. 854-855; “Bessel-integral functions,” Edin. Math. So., Proc., s. 2, v. 3, 1933, p. 276-285. A. H. A. Hogg, “Equilibrium of a thin plate, symmetrically loaded, resting on an elastic foundation of infinite depth,” Phil. Mag., s. 7, v. 25, 1938, p. 576-582.
  • V. G. Smith, An asymptotic expansion of $Ji_0(x)=\int ^\infty _x(J_0(t)/t)dt$, J. Math. Phys. Mass. Inst. Tech. 22 (1943), 58–59. MR 8705, DOI 10.1002/sapm194322158
  • N. E. Nörlund, MĂ©moire sur les polynomes de bernoulli, Acta Math. 43 (1922), no. 1, 121–196 (French). MR 1555176, DOI 10.1007/BF02401755
  • L. M. Milne-Thomson, The Calculus of Finite Differences, Macmillan & Co., Ltd., London, 1951. MR 0043339
  • H. T. Davis, Tables of the Higher Mathematical Functions, Bloomington, Ind., The Principia Press, v. 2, 1935, p. 208-210. P. S. de Laplace, “MĂ©moire sur l’intĂ©gration des Ă©quations diffĂ©rentielles par approximation,” MĂ©m. Acad. roy. sci., Paris, 1780, or Oeuvres, v. 9, p. 357-380, especially p. 359-362, 372-374. A Semi-Centennial History of the American Mathematical Society 1888-1938, New York, 1938, p. 119-120. Helge von Koch, “Sur une application des dĂ©terminants infinis Ă  la thĂ©orie des Ă©quations differentielles linĂ©aires,” Acta Math., v. 15, 1891, p. 53-63; “Sur les dĂ©terminants infinis et les Ă©quations differentielles linĂ©aires,” Acta Math., v. 16, 1892-3, p. 217-295. Rayleigh, “On maintained vibrations,” Phil. Mag., s. 4, v. 15, 1883, p. 229-235, or Scientific Papers, v. 2, 1900, p. 188-193; “On the maintenance of vibrations by forces of double frequency, and on the propagation of waves through a medium endowed with a periodic structure,” Phil. Mag., s. 4, v. 24, 1887, p. 145-159, or Scientific Papers, v. 3, 1902, p. 1-14. G. LamĂ©, “MĂ©emoire sur les surfaces isothermes dans les corps solides homogĂšnes en Ă©quilibre de tempĂ©rature,” Jn. de Math., s. 1, v. 2, 1837, p. 147-188; “MĂ©moire sur l’équilibre des tempĂ©ratures, dans les corps solides homogĂšnes . . .,” Jn. de Math., s. 1, v. 4, 1839, p. 126-163, 351-385. E. L. Mathieu, “MĂ©moire sur le mouvement vibratoire d’une membrane de forme elliptique,” Jn. de Math., s. 2, v. 13, 1868, p. 137-203; Cours de Physique MathĂ©matique, Paris, 1873. C. Niven, “On the conduction of heat in ellipsoids of revolution,” R. So. London, Trans., v. 171, 1880, p. 117-151. Heine, Handbuch der Kugelfunktionen, second ed., Berlin, v. 2, 1881. M. Brillouin, Propagation de l’ÉlectricitĂ©, Paris, Hermann, 1904, Ch. 6, p. 376, 383-4, etc.
  • Egil A. Hylleraas, Équation d’ondes d’un Ă©lectron dans le champ de forces de deux noyaux atomiques ProblĂšme de l’ion molĂ©culaire d’hydrogĂšne, Ann. Inst. H. PoincarĂ© 7 (1937), no. 3, 121–153 (French). MR 1508038
  • E. T. Whittaker, “On the functions associated with the elliptic cylinder in harmonic analysis,” Intern. Congress Math., Cambridge, 1912, v. 1, p. 366-371. “On Lame’s differential equation and ellipsoidal harmonics,” London Math. So., Proc., s. 2, v. 14, 1915, p. 260-268 or Modern Analysis, p. 564; “On an integral equation whose solutions are the functions of LamĂ©,” R. So. Edinburgh, Proc., v. 35,1915, p. 70-77. See also J. H. Priestley, “On some solutions of the wave equation,” London Math. So., Proc., s. 2, v. 20, 1922, p. 37-50. J. L. Sharma, Jn. de Math., s. 9, v. 16, 1937, p. 199-203, 355-360. N. Nielsen, ThĂ©orie des Fonctions MetasphĂ©riques, Paris, 1911. R. C. Maclaurin, “On the solutions of the equation $({\nabla ^2} + k)\psi = 0$ in elliptic coordinates and their physical applications,” Cambridge Phil. So., Trans., v. 17, 1898, p. 41-108. For numerical results see p. 92-95, 98, 106, 108. L. Page and N. I. Adams, Jr., “The electrical oscillations of a prolate spheroid, part I,” Phys. Rev., s. 2, v. 53, 1938, p. 819-831.
Additional Information
  • © Copyright 1944 American Mathematical Society
  • Journal: Math. Comp. 1 (1944), 142-160
  • DOI: https://doi.org/10.1090/S0025-5718-44-99051-4