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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

On the numerators of the convergents of the Stieltjes continued fractions


Author: Jacob Sherman
Journal: Trans. Amer. Math. Soc. 35 (1933), 64-87
MSC: Primary 40A15; Secondary 30B70
MathSciNet review: 1501672
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  • [1] Stieltjes, Recherches sur les fractions continues, Oeuvres, vol. 2, pp. 398-566.
  • [2] O. Perron, Die Lehre von den Kettenbrüchen, 2d edition, 1929, Chapters VII, VIII, IX.
  • [3] Hans Hamburger, Über eine Erweiterung des Stieltjesschen Momentenproblems, Math. Ann. 82 (1921), no. 3-4, 168–187 (German). MR 1511981, http://dx.doi.org/10.1007/BF01498663
  • [4] J. Shohat and J. Sherman, On the numerators..., Proceedings of the National Academy of Sciences, vol. 18 (1932), pp. 283-287.
  • [5] Jacques Chokhate (J. Shohat), Sur le développement de l'intégrale
    $\displaystyle \int_a^b {\frac{{p(y)dy}}{{x - y}} \cdots ,} $
    Rendiconti di Palermo, vol. 47 (1923), pp. 25-46.
  • [6] J. Shohat, On Stieltjes Continued Fractions, Amer. J. Math. 54 (1932), no. 1, 79–84. MR 1506874, http://dx.doi.org/10.2307/2371078
  • [7] Jacques Chokhate (J. Shohat), Sur une classe étendue de fractions continues..., Comptes Rendus, vol. 191 (1930), p. 988.
  • [8] Christoffel, Über die Gaussische Quadratur..., Crelle, vol. 55 (1858), pp. 61-83, where the differential equation for the Legendre case $ \alpha = \beta = 1$ is obtained in an entirely different manner.
  • [9] P. Appell et J. Kampé de Fériet, Fonctions Hypergéométriques et Hypersphériques. Polynomes d'Hermite, Paris, 1926, p. 338.
  • [10] C. Possé, Sur quelques Applications des Fractions Continues Algébriques, St. Petersbourg, 1886.
  • [11] T. Carleman, Sur la résolution de certaines équations intégrales, Arkiv för Matematik, Astronomi och Fysik, vol. 16 (1922), No. 26.

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1933-1501672-3
PII: S 0002-9947(1933)1501672-3
Article copyright: © Copyright 1933 American Mathematical Society