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Transactions of the American Mathematical Society

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A new class of continued fraction expansions for the ratios of hypergeometric functions


Author: Evelyn Franik
Journal: Trans. Amer. Math. Soc. 81 (1956), 453-476
MSC: Primary 33.0X
DOI: https://doi.org/10.1090/S0002-9947-1956-0076937-0
MathSciNet review: 0076937
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  • [1a] L. Euler. De fractionibus continuis, Introductio in analysin infinitorum, Chapter 18, vol. 1, 1748 (Opera Omnia, Series Prima, vol. 8, pp. 362-390).
  • [1] E. Frank, On the properties of certain continued fractions, Proc. Amer. Math. Soc. vol. 3 (1952) pp. 921-937. MR 0052537 (14:635a)
  • [2] C. F. Gauss, Disquisitiones generates circa seriem infinitam $ 1 + \alpha \beta x/1 \cdot \gamma + \alpha (\alpha + 1)\beta (\beta + 1)xx/1 \... ... \cdot 2 \cdot 3 \cdot \gamma (\gamma + 1)(\gamma + 2) + {\text{etc}}{\text{.}}$, Werke, vol. 3, 1876, pp. 125-162.
  • [3] O. Perron, Die Lehre von den Kettenbrüchen, Leipzig, Teubner, 1929.
  • [4] -, Die Lehre von den Kettenbrüchen, vol. 2, Stuttgart, to be published by Teubner.
  • [5] L. Schlesinger, Handbuch der Theorie der linearen Differentialgleichungen, vol. 1, Leipzig, Teubner, 1895.
  • [6] E. B. Van Vleck, On the convergence of algebraic continued fractions whose coefficients have limiting values, Trans. Amer. Math. Soc. vol. 5 (1904) pp. 253-262. MR 1500672

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DOI: https://doi.org/10.1090/S0002-9947-1956-0076937-0
Article copyright: © Copyright 1956 American Mathematical Society

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