Pringsheim theorem for continued fractions

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11: 4.39 Continued Fractions

§4.39 Continued Fractions

… ►For these and other continued fractions involving inverse hyperbolic functions see Lorentzen and Waadeland (1992, pp. 569–571). …

12: 1.10 Functions of a Complex Variable

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Picard’s Theorem

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§1.10(iv) Residue Theorem

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Rouché’s Theorem

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Lagrange Inversion Theorem

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Extended Inversion Theorem

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13: 10.10 Continued Fractions

§10.10 Continued Fractions

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14: 10.33 Continued Fractions

§10.33 Continued Fractions

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15: 10.74 Methods of Computation

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§10.74(v) Continued Fractions

►For applications of the continued-fraction expansions (10.10.1), (10.10.2), (10.33.1), and (10.33.2) to the computation of Bessel functions and modified Bessel functions see Gargantini and Henrici (1967), Amos (1974), Gautschi and Slavik (1978), Tretter and Walster (1980), Thompson and Barnett (1986), and Cuyt et al. (2008). … ►To ensure that no zeros are overlooked, standard tools are the phase principle and Rouché’s theorem; see §1.10(iv). …

16: 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 … … ►Markov’s theorem states that … ►See Szegő (1975, Theorem 7.2). …

17: 4.25 Continued Fractions

§4.25 Continued Fractions

… ►See Lorentzen and Waadeland (1992, pp. 560–571) for other continued fractions involving inverse trigonometric functions. …

18: Bibliography R

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Normal limit theorems for symmetric random matrices. Probab. Theory Related Fields 112 (3), pp. 411–423.

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External Links:

ISSN 0178-8051, Document, MathReview (Alexei Khorunzhy), ZentralBlatt

Referenced by:

§35.9.

Encodings:

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A code to calculate (high order) Bessel functions based on the continued fractions method. Comput. Phys. Comm. 76 (3), pp. 381–388.

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Notes:

Double-precision Fortran, maximum accuracy 18D.

External Links:

ISSN 0010-4655, Document, Code, MathReview, ZentralBlatt

Referenced by:

6th item.

Encodings:

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13 Lectures on Fermat’s Last Theorem. Springer-Verlag, New York.

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External Links:

ISBN 0-387-90432-8, MathReview (T. Metsänkylä), ZentralBlatt

Referenced by:

§24.10(iv), §24.17(iii).

Encodings:

BibTeX

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Partial fractions expansions and identities for products of Bessel functions. J. Math. Phys. 46 (4), pp. 043509–1–043509–18.

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External Links:

ISSN 0022-2488, Document, MathReview (Wolfgang zu Castell), ZentralBlatt

Referenced by:

§10.23(ii).

Encodings:

BibTeX

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Dawson’s integral and the sampling theorem. Computers in Physics 3 (2), pp. 85–87.

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Referenced by:

§7.25(vi).

Encodings:

BibTeX

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19: 10.23 Sums

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§10.23(i) Multiplication Theorem

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§10.23(ii) Addition Theorems

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Neumann’s Addition Theorem

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Graf’s and Gegenbauer’s Addition Theorems

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20: 7.9 Continued Fractions

§7.9 Continued Fractions

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