A new class of continued fraction expansions for the ratios of hypergeometric functions
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- by Evelyn Franik
- Trans. Amer. Math. Soc. 81 (1956), 453-476
- DOI: https://doi.org/10.1090/S0002-9947-1956-0076937-0
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References
- L. Euler. De fractionibus continuis, Introductio in analysin infinitorum, Chapter 18, vol. 1, 1748 (Opera Omnia, Series Prima, vol. 8, pp. 362-390).
- Evelyn Frank, On the properties of certain continued fractions, Proc. Amer. Math. Soc. 3 (1952), 921–937. MR 52537, DOI 10.1090/S0002-9939-1952-0052537-5 C. F. Gauss, Disquisitiones generates circa seriem infinitam $1 + \alpha \beta x/1 \cdot \gamma + \alpha (\alpha + 1)\beta (\beta + 1)xx/1 \cdot 2 \cdot \gamma (\gamma + 1) + \alpha (\alpha + 1)(\alpha + 2)\beta (\beta + 1)(\beta + 2) \cdot {x^3}/1 \cdot 2 \cdot 3 \cdot \gamma (\gamma + 1)(\gamma + 2) + {\text {etc}}{\text {.}}$, Werke, vol. 3, 1876, pp. 125-162. O. Perron, Die Lehre von den Kettenbrüchen, Leipzig, Teubner, 1929. —, Die Lehre von den Kettenbrüchen, vol. 2, Stuttgart, to be published by Teubner. L. Schlesinger, Handbuch der Theorie der linearen Differentialgleichungen, vol. 1, Leipzig, Teubner, 1895.
- Edward B. Van Vleck, On the convergence of algebraic continued fractions whose coefficients have limiting values, Trans. Amer. Math. Soc. 5 (1904), no. 3, 253–262. MR 1500672, DOI 10.1090/S0002-9947-1904-1500672-9
Bibliographic Information
- © Copyright 1956 American Mathematical Society
- 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