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11: 4.37 Inverse Hyperbolic Functions

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12: Bibliography O

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Triorthogonal systems in spaces of constant curvature in which the equation ${\mathrm{\Delta }}_{2}u+\lambda u=0$ allows a complete separation of variables. Mat. Sbornik N.S. 27(69) (3), pp. 379–426 (Russian).

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Notes:

In Russian.

External Links:

MathReview (H. Busemann), ZentralBlatt

Referenced by:

§31.17(i).

Encodings:

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13: Bibliography T

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Parabolic cylinder functions $U(n,x)$ for natural $n$ and positive $x$ . Comput. Phys. Commun. 69, pp. 415–419.

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Notes:

Double-precision Fortran, minimum accuracy 14S, maximum accuracy 21D.

External Links:

Document, Code

Referenced by:

4th item.

Encodings:

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14: Bibliography S

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Parabolic cylinder functions of integer and half-integer orders for nonnegative arguments. Comput. Phys. Comm. 115 (1), pp. 69–86.

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Notes:

Double-precision Fortran, minimum accuracy 14S, maximum accuracy 18D.

External Links:

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

Referenced by:

3rd item.

Encodings:

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On an identity of Ramanujan based on the hypergeometric series ${}_2{}^{}F_1^{}(\frac{1}{3},\frac{2}{3};\frac{1}{2};x)$ . J. Number Theory 69 (2), pp. 125–134.

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External Links:

ISSN 0022-314X, Document, MathReview (Bruce C. Berndt), ZentralBlatt

Referenced by:

§20.11(iii).

Encodings:

BibTeX

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Staudt and arithmetical properties of Bernoulli numbers. Historia Sci. (2) 5 (1), pp. 69–74.

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External Links:

ISSN 0285-4821, MathReview (Peter M. Neumann), ZentralBlatt

Referenced by:

§24.10(ii).

Encodings:

BibTeX

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15: 14.17 Integrals

… ►For Mellin transforms involving associated Legendre functions see Oberhettinger (1974, pp. 69–82) and Marichev (1983, pp. 247–283), and for inverse transforms see Oberhettinger (1974, pp. 205–215).

16: Bibliography F

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The third Appell function for one large variable. J. Approx. Theory 165, pp. 60–69.

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External Links:

ISSN 0021-9045, Document, FullText, MathReview Entry, ZentralBlatt

Referenced by:

§16.13, §16.13.

Encodings:

BibTeX

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17: 4.23 Inverse Trigonometric Functions

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18: Bibliography

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Szegő Type Asymptotics for the Reproducing Kernel in Spaces of Full-Plane Weighted Polynomials. Comm. Math. Phys. 398 (3), pp. 1291–1348.

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External Links:

ISSN 0010-3616, Document, Link, MathReview Entry, ZentralBlatt

Referenced by:

§8.11(iii), §8.11(iii), Erratum (V1.1.10) for Section 8.11(iii).

Encodings:

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19: Bibliography D

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Über die Bestimmung der mittleren Werthe in der Zahlentheorie. Abhandlungen der Königlich Preussischen Akademie der Wissenschaften von 1849, pp. 69–83 (German).

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Notes:

Reprinted in G. Lejeune Dirichlet’s Werke, Band II, pp. 49–66, Reimer, Berlin, 1897 and with corrections in G. Lejeune Dirichlet’s Werke, AMS Chelsea Publishing Series, Providence, RI, 1969.

External Links:

ISBN 0-8284-0225-6, Link, MathReview

Referenced by:

§27.11.

Encodings:

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20: 1.9 Calculus of a Complex Variable

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