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A new class of continued fraction expansions for the ratios of Heine functions. II


Author: Evelyn Frank
Journal: Trans. Amer. Math. Soc. 95 (1960), 17-26
MSC: Primary 33.00
DOI: https://doi.org/10.1090/S0002-9947-1960-0116105-8
MathSciNet review: 0116105
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  • [1] E. Frank, A new class of continued fraction expansions for the ratios of Heine functions, Trans. Amer. Math. Soc. vol. 88 (1958) pp. 288-300. MR 0097549 (20:4017)
  • [2] -, A new class of continued fraction expansions for the ratios of hypergeometric functions, Trans. Amer. Math. Soc. vol. 81 (1956) pp. 453-476. MR 0076937 (17:967e)
  • [3] E. Heine, Über die Reihe
    $\displaystyle 1 + \frac{{({q^\alpha } - 1)({q^\beta } - 1)}} {{(q - 1)({q^\gamm... ...} {{(q - 1)({q^2} - 1)({q^\gamma } - 1)({q^{\gamma + 1}} - 1)}}{z^2} + \cdots ,$
    Jrn. für Math. vol. 32 (1846) pp. 210-212.
  • [4] -, Untersuchungen über die Reihe
    $\displaystyle 1 + \frac{{(1 - {q^\alpha })(1 - {q^\beta })}} {{(1 - q)(1 - {q^\... ...}} {{(1 - q)(1 - {q^2})(1 - {q^\gamma })(1 - {q^{\gamma + 1}})}}{z^2} + \cdots $
    Jrn. für Math. vol. 34 (1847) pp. 285-328.
  • [5] -, Handbuch der Kugelfunctionen, vol. 1, Berlin, Reimer, 1878.
  • [6] O. Perron, Die Lehre von den Kettenbrüchen, vol. 2, 3d. ed., Stuttgart, Teubner, 1957. MR 0085349 (19:25c)

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DOI: https://doi.org/10.1090/S0002-9947-1960-0116105-8
Article copyright: © Copyright 1960 American Mathematical Society

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