continued fraction

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41: Bibliography T

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COULCC: A continued-fraction algorithm for Coulomb functions of complex order with complex arguments. Comput. Phys. Comm. 36 (4), pp. 363–372.

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Notes:

Double-precision Fortran, minimum accuracy: 14D. See also Thompson (2004)

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Document, Code, ZentralBlatt

Referenced by:

1st item, §33.23(vi), 3rd item.

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Erratum to “COULCC: A continued-fraction algorithm for Coulomb functions of complex order with complex arguments”. Comput. Phys. Comm. 159 (3), pp. 241–242.

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External Links:

Document, Code, ZentralBlatt

Referenced by:

§33.23(vi), I. J. Thompson and A. R. Barnett (1985).

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42: 6.18 Methods of Computation

… ►Lastly, the continued fraction (6.9.1) can be used if $|z|$ is bounded away from the origin. …

43: 13.31 Approximations

… ►For a discussion of the convergence of the Padé approximants that are related to the continued fraction (13.5.1) see Wimp (1985). …

44: 31.4 Solutions Analytic at Two Singularities: Heun Functions

… ►The eigenvalues $q_m$ satisfy the continued-fraction equation …

45: 8.19 Generalized Exponential Integral

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§8.19(vii) Continued Fraction

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46: 28.6 Expansions for Small $q$

… ►Higher coefficients in the foregoing series can be found by equating coefficients in the following continued-fraction equations: …

47: 16.4 Argument Unity

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§16.4(iv) Continued Fractions

►For continued fractions for ratios of ${}_3{}^{}F_2^{}$ functions with argument unity, see Cuyt et al. (2008, pp. 315–317). …

48: Bibliography C

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On Stieltjes’ continued fraction for the gamma function. Math. Comp. 34 (150), pp. 547–551.

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External Links:

ISSN 0025-5718, FullText, MathReview, ZentralBlatt

Referenced by:

§5.10.

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Numerical integration of related Hankel transforms by quadrature and continued fraction expansion. Geophysics 48 (12), pp. 1671–1686.

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Notes:

Fortran code.

External Links:

ISSN 0098-3500, Document

Referenced by:

§10.77(ix).

Encodings:

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Handbook of Continued Fractions for Special Functions. Kluwer Academic Publishers Group, Dordrecht.

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Referenced by:

Profile Annie A. M. Cuyt.

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Handbook of Continued Fractions for Special Functions. Springer, New York.

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External Links:

ISBN 978-1-4020-6948-2, MathReview Entry, ZentralBlatt

Referenced by:

§10.10, §10.33, §10.55, §10.74(v), §12.6, §13.17, §13.5, §15.7, §16.4(iv), §17.6(vi), §17.7(ii), §18.13, §3.10(ii), §3.10(iii), §4.25, §4.39, §4.9(i), §4.9(ii), §4.9(iii), §5.10, §5.15, §6.9, §7.18(v), §7.22(i), §7.9, §8.17(v), §8.19(vii), §8.9.

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49: 18.2 General Orthogonal Polynomials

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§18.2(x) Orthogonal Polynomials and Continued Fractions

… ►Using the terminology of §1.12(ii), the $n$-th approximant of the continued fraction …

50: Bibliography L

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Generating Bessel functions in Mie scattering calculations using continued fractions. Applied Optics 15 (3), pp. 668–671.

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Referenced by:

§3.10(iii), §3.10(iii), Erratum (V1.0.24) for Paragraph Steed’s Algorithm (in §3.10(iii)).

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Continued Fractions with Applications. Studies in Computational Mathematics, North-Holland Publishing Co., Amsterdam.

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External Links:

ISBN 0-444-89265-6, MathReview (Olav Njåstad), ZentralBlatt

Referenced by:

§1.12(ii), §1.12(iv), §1.12(v), §15.7, §18.13, §3.10(ii), §3.10(iii), §3.11(iv), §4.25, §4.39, §4.9(i), §4.9(ii), §5.10, §6.9, §7.18(v), §7.9.

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