This is a preview of subscription content, access via your institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
Bibliography
Erdélyi, A., W. Magnus, F. Oberhettinger and F. G. Tricomi: Higher transcendental functions. I. (Based, in part, on notes left by Harry Bateman, and compiled by the Staff of the Bateman Manuscript Project).-McGraw-Hill Book Company, Inc., New York / Toronto / London, 1953.
Frank, E.: A new class of continued fraction expansions for the ratios of hypergeometric functions.-Trans. Amer. Math. Soc. 81, 1956, pp.453–476.
New continued fraction expansions for the ratios of hypergeometric functions.-Univ. Lisboa Revista Fac. Ci. (2) A 7, 1959, pp.301–310.
Gauß, C. F.: Disquisitiones generales circa seriem infinitam \(1 + \frac{{\alpha \beta }}{{1.\gamma }}x + \frac{{\alpha (\alpha + 1) \beta (\beta + 1)}}{{1.2.\gamma (\gamma + 1)}} x x + \frac{{\alpha (\alpha + 1) (\alpha + 2) \beta (\beta + 1) (\beta + 2)}}{{1.2.3.\gamma (\gamma + 1) (\gamma + 1) (\gamma + 2)}} x^3 + etc.\). Pars prior.-Commentations societatis regiae scientiarum Gottingenesis recentiores. II, Gottingae MDCCCXIII.=Werke. III. [2. Abdruck], pp.123–162. Königliche Gesellschaft der Wissenschaften zu Göttingen, Göttingen, 1876.
Perron, O.: Die Lehre von den Kettenbrüchen. I. Elementare Kettenbrüche.-[Dritte Auflage.] B. G. Teubner, Verlagsgesellschaft, Stuttgart, 1954.
Die Lehre von den Kettenbrüchen. II. Analytisch-funktionentheoretische Kettenbrüche.-[Dritte Auflage.] B. G. Teubner, Verlagsgesellschaft, Stuttgart, 1957.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1974 Springer-Verlag
About this paper
Cite this paper
Frank, E. (1974). Continued fraction expansions for the ratios of hypergeometric functions evaluated on computers. In: Lehto, O., Louhivaara, I.S., Nevanlinna, R. (eds) Topics in Analysis. Lecture Notes in Mathematics, vol 419. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0064717
Download citation
DOI: https://doi.org/10.1007/BFb0064717
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-06965-2
Online ISBN: 978-3-540-37907-2
eBook Packages: Springer Book Archive
