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1: 13.5 Continued Fractions
For more details on how a continued fraction converges to a meromorphic function see Jones and Thron (1980). …
2: 13.17 Continued Fractions
For more details on how a continued fraction converges to a meromorphic function see Jones and Thron (1980). …
3: Bibliography J
  • L. Jacobsen, W. B. Jones, and H. Waadeland (1986) Further results on the computation of incomplete gamma functions. In Analytic Theory of Continued Fractions, II (Pitlochry/Aviemore, 1985), W. J. Thron (Ed.), Lecture Notes in Math. 1199, pp. 67–89.
  • W. B. Jones and W. J. Thron (1974) Numerical stability in evaluating continued fractions. Math. Comp. 28 (127), pp. 795–810.
  • W. B. Jones and W. J. Thron (1985) On the computation of incomplete gamma functions in the complex domain. J. Comput. Appl. Math. 12/13, pp. 401–417.
  • W. B. Jones and W. J. Thron (1980) Continued Fractions: Analytic Theory and Applications. Encyclopedia of Mathematics and its Applications, Vol. 11, Addison-Wesley Publishing Co., Reading, MA.
  • 4: 5.10 Continued Fractions
    Also see Cuyt et al. (2008, pp. 223–228), Jones and Thron (1980, pp. 348–350), Lorentzen and Waadeland (1992, pp. 221–224), and Jones and Van Assche (1998).
    5: 8.9 Continued Fractions
    For these expansions and further information see Jones and Thron (1985). …
    6: 8.25 Methods of Computation
    The computation of γ ( a , z ) and Γ ( a , z ) by means of continued fractions is described in Jones and Thron (1985) and Gautschi (1979b, §§4.3, 5). …
    7: Possible Errors in DLMF
    Errors in the printed Handbook may already have been corrected in the online version; please consult Errata. …
    8: 4.25 Continued Fractions
    4.25.1 tan z = z 1 z 2 3 z 2 5 z 2 7 , z ± 1 2 π , ± 3 2 π , .
    4.25.2 tan ( a z ) = a tan z 1 + ( 1 a 2 ) tan 2 z 3 + ( 4 a 2 ) tan 2 z 5 + ( 9 a 2 ) tan 2 z 7 + , | z | < 1 2 π , a z ± 1 2 π , ± 3 2 π , .
    9: How to Cite
    The direct correspondence between the reference numbers in the printed Handbook and the permalinks used online in the DLMF enables readers of either version to cite specific items and their readers to easily look them up again — in either version! The following table outlines the correspondence between reference numbers as they appear in the Handbook, and the URL’s that find the same item online. …
    10: 1.12 Continued Fractions