A new class of continued fraction expansions for the ratios of Heine functions. II
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- by Evelyn Frank PDF
- Trans. Amer. Math. Soc. 95 (1960), 17-26 Request permission
References
- Evelyn Frank, A new class of continued fraction expansions for the ratios of Heine functions, Trans. Amer. Math. Soc. 88 (1958), 288–300. MR 97549, DOI 10.1090/S0002-9947-1958-0097549-0
- Evelyn Frank, A new class of continued fraction expansions for the ratios of hypergeometric functions, Trans. Amer. Math. Soc. 81 (1956), 453–476. MR 76937, DOI 10.1090/S0002-9947-1956-0076937-0 E. Heine, Über die Reihe \[ 1 + \frac {{({q^\alpha } - 1)({q^\beta } - 1)}} {{(q - 1)({q^\gamma } - 1)}}z + \frac {{({q^\alpha } - 1)({q^{\alpha + 1}} - 1)({q^\beta } - 1)({q^{\beta + 1}} - 1)}} {{(q - 1)({q^2} - 1)({q^\gamma } - 1)({q^{\gamma + 1}} - 1)}}{z^2} + \cdots ,\] Jrn. für Math. vol. 32 (1846) pp. 210-212. —, Untersuchungen über die Reihe \[ 1 + \frac {{(1 - {q^\alpha })(1 - {q^\beta })}} {{(1 - q)(1 - {q^\gamma })}}z + \frac {{(1 - {q^\alpha })(1 - {q^{\alpha + 1}})(1 - {q^\beta })(1 - {q^{\beta + 1}})}} {{(1 - q)(1 - {q^2})(1 - {q^\gamma })(1 - {q^{\gamma + 1}})}}{z^2} + \cdots \] Jrn. für Math. vol. 34 (1847) pp. 285-328. —, Handbuch der Kugelfunctionen, vol. 1, Berlin, Reimer, 1878.
- Oskar Perron, Die Lehre von den Kettenbrüchen. Dritte, verbesserte und erweiterte Aufl. Bd. II. Analytisch-funktionentheoretische Kettenbrüche, B. G. Teubner Verlagsgesellschaft, Stuttgart, 1957 (German). MR 0085349
Additional Information
- © Copyright 1960 American Mathematical Society
- 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