Van Vleck theorem for continued fractions

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31: Bibliography H

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Tables of Radial Spheroidal Wave Functions, Vols. 1-3, Prolate, $m=0,1,2$; Vols. 4-6, Oblate, $m=0,1,2$ . Technical report Naval Research Laboratory, Washington, D.C..

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Notes:

NRL Reports 7088-7093

External Links:

ZentralBlatt

Referenced by:

3rd item.

Encodings:

BibTeX

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Orthogonal Laurent polynomials. Nederl. Akad. Wetensch. Indag. Math. 48 (1), pp. 17–36.

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External Links:

ISSN 0019-3577, Document, MathReview (W. J. Thron), ZentralBlatt

Referenced by:

§18.33(v).

Encodings:

BibTeX

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Applied and Computational Complex Analysis. Vol. 2: Special Functions—Integral Transforms—Asymptotics—Continued Fractions. Wiley-Interscience [John Wiley & Sons], New York.

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Notes:

Reprinted in 1991.

External Links:

ISBN 0-471-01525-3, MathReview (A. E. Heins), ZentralBlatt

Referenced by:

§1.11(v), Ch.3.

Encodings:

BibTeX

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32: 28.27 Addition Theorems

§28.27 Addition Theorems

►Addition theorems provide important connections between Mathieu functions with different parameters and in different coordinate systems. They are analogous to the addition theorems for Bessel functions (§10.23(ii)) and modified Bessel functions (§10.44(ii)). …

33: 3.10 Continued Fractions

§3.10 Continued Fractions

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Stieltjes Fractions

►A continued fraction of the form … ►

Jacobi Fractions

… ►The continued fraction …

34: 25.10 Zeros

… ►Also, $\zeta \left(s\right)\ne 0$ for $\mathrm{\Re }s=1$, a property first established in Hadamard (1896) and de la Vallée Poussin (1896a, b) in the proof of the prime number theorem (25.16.3). … ►Calculations based on the Riemann–Siegel formula reveal that the first ten billion zeros of $\zeta \left(s\right)$ in the critical strip are on the critical line (van de Lune et al. (1986)). …

35: 6.9 Continued Fraction

§6.9 Continued Fraction

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36: 18.13 Continued Fractions

§18.13 Continued Fractions

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Chebyshev

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Legendre

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Laguerre

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Hermite

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37: 21.10 Methods of Computation

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Deconinck and van Hoeij (2001). Here a plane algebraic curve representation of the Riemann surface is used.

38: 28.36 Software

… ►See also Clemm (1969), Delft Numerical Analysis Group (1973), Rengarajan and Lewis (1980), Van Buren and Boisvert (2007), and Ziener et al. (2012).

39: 34.7 Basic Properties: $\mathit{9}j$ Symbol

… ►For generating functions for the $\mathit{9}j$ symbol see Biedenharn and van Dam (1965, p. 258, eq. (4.37)). … ►It constitutes an addition theorem for the $\mathit{9}j$ symbol. …

40: 27.18 Methods of Computation: Primes

… ►A practical version is described in Bosma and van der Hulst (1990). …