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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48 .

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On the numerators of the convergents of the Stieltjes continued fractions
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by Jacob Sherman PDF
Trans. Amer. Math. Soc. 35 (1933), 64-87 Request permission
References
    Stieltjes, Recherches sur les fractions continues, Oeuvres, vol. 2, pp. 398-566. O. Perron, Die Lehre von den Kettenbrüchen, 2d edition, 1929, Chapters VII, VIII, IX.
  • Hans Hamburger, Über eine Erweiterung des Stieltjesschen Momentenproblems, Math. Ann. 82 (1921), no. 3-4, 168–187 (German). MR 1511981, DOI 10.1007/BF01498663
  • J. Shohat and J. Sherman, On the numerators…, Proceedings of the National Academy of Sciences, vol. 18 (1932), pp. 283-287. Jacques Chokhate (J. Shohat), Sur le développement de l’intégrale \[ \int _a^b {\frac {{p(y)dy}}{{x - y}} \cdots ,} \] Rendiconti di Palermo, vol. 47 (1923), pp. 25-46.
  • J. Shohat, On Stieltjes Continued Fractions, Amer. J. Math. 54 (1932), no. 1, 79–84. MR 1506874, DOI 10.2307/2371078
  • Jacques Chokhate (J. Shohat), Sur une classe étendue de fractions continues…, Comptes Rendus, vol. 191 (1930), p. 988. 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. P. Appell et J. Kampé de Fériet, Fonctions Hypergéométriques et Hypersphériques. Polynomes d’Hermite, Paris, 1926, p. 338. C. Possé, Sur quelques Applications des Fractions Continues Algébriques, St. Petersbourg, 1886. 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
  • © Copyright 1933 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 35 (1933), 64-87
  • MSC: Primary 40A15; Secondary 30B70
  • DOI: https://doi.org/10.1090/S0002-9947-1933-1501672-3
  • MathSciNet review: 1501672