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11: Bibliography I

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The zeros of regular Coulomb wave functions and of their derivatives. Math. Comp. 29, pp. 878–887.

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External Links:

ISSN 0025-5718, Document, MathReview, ZentralBlatt

Referenced by:

§3.8(iii).

Encodings:

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An integral which occurs in statistics. Proceedings of the Cambridge Philosophical Society 29, pp. 271–276.

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External Links:

Document, ZentralBlatt

Referenced by:

§35.3(i), §35.3(ii).

Encodings:

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Highly Oscillatory Quadrature: The Story So Far. In Numerical Mathematics and Advanced Applications, A. Bermudez de Castro and others (Eds.), pp. 97–118.

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Notes:

Proceedings of ENuMath, Santiago de Compostela (2005)

External Links:

ISBN 3-540-34287-7, MathReview, ZentralBlatt

Referenced by:

§3.5(vii).

Encodings:

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Connection formulae for the fourth Painlevé transcendent; Clarkson-McLeod solution. J. Phys. A 31 (17), pp. 4073–4113.

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External Links:

ISSN 0305-4470, Document, MathReview (Yoshitsugu Takei), ZentralBlatt

Referenced by:

§32.11(v).

Encodings:

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Quantum Field Theory. International Series in Pure and Applied Physics, McGraw-Hill International Book Co., New York.

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Notes:

Reprinted by Dover, 2006.

External Links:

ISBN 0-07-032071-3, MathReview (V. E. Korepin)

Referenced by:

§22.19(ii).

Encodings:

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12: Bibliography

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Asymptotic expansions of spheroidal wave functions. J. Math. Phys. Mass. Inst. Tech. 28, pp. 195–199.

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External Links:

MathReview (J. G. van der Corput), ZentralBlatt

Referenced by:

§30.9(iii).

Encodings:

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On the zeros of confluent hypergeometric functions. III. Characterization by means of nonlinear equations. Lett. Nuovo Cimento (2) 29 (11), pp. 353–358.

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External Links:

ISSN 0024-1318, MathReview (James M. Horner)

Referenced by:

§13.9(i).

Encodings:

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Bernoulli’s power-sum formulas revisited. Math. Gaz. 90 (518), pp. 276–279.

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Referenced by:

§24.4(iii).

Encodings:

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Elliptic Functions. London Mathematical Society Student Texts, Vol. 67, Cambridge University Press, Cambridge.

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External Links:

ISBN 978-0-521-78078-0; 978-0-521-78563-1; 0-521-78563-4, Document, MathReview (Shaun Cooper), ZentralBlatt

Referenced by:

Ch.19, Ch.20, Ch.22, Ch.23.

Encodings:

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Normal forms of functions in the neighborhood of degenerate critical points. Uspehi Mat. Nauk 29 (2(176)), pp. 11–49 (Russian).

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Notes:

Collection of articles dedicated to the memory of Ivan Georgievič Petrovskiĭ (1901–1973), I. In Russian. English translation: Russian Math. Surveys, 29(1974), no. 2, pp. 10–50.

External Links:

Document, MathReview (G. R. Belickii), ZentralBlatt

Referenced by:

§36.2(i).

Encodings:

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13: Bibliography D

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Computing spectra of linear operators using the Floquet-Fourier-Hill method. J. Comput. Phys. 219 (1), pp. 296–321.

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External Links:

ISSN 0021-9991, MathReview, ZentralBlatt

Referenced by:

§22.11.

Encodings:

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Accurate and efficient evaluation of Schur and Jack functions. Math. Comp. 75 (253), pp. 223–239.

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Notes:

For Fortran software for these functions, see Plamen Koev’s home page.

External Links:

Home Page, ISSN 0025-5718, Document, MathReview Entry, ZentralBlatt

Referenced by:

1st item.

Encodings:

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Integral representations for elliptic functions. J. Math. Anal. Appl. 316 (1), pp. 142–160.

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External Links:

ISSN 0022-247X, Document, MathReview Entry, ZentralBlatt

Referenced by:

§23.11.

Encodings:

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Uniform asymptotic approximations for incomplete Riemann zeta functions. J. Comput. Appl. Math. 190 (1-2), pp. 339–353.

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External Links:

ISSN 0377-0427, Document, MathReview Entry, ZentralBlatt

Referenced by:

§8.22(ii).

Encodings:

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The incomplete beta function—a historical profile. Arch. Hist. Exact Sci. 24 (1), pp. 11–29.

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External Links:

ISSN 0003-9519, MathReview (Willard Parker), ZentralBlatt

Referenced by:

§8.17(i).

Encodings:

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14: Christopher J. Howls

… ►Since 2006 he has served as Chair of the Standing Committee of the British Applied Mathematics Colloquium. …

15: Alexander A. Its

… ► Novokshënov), published by the American Mathematical Society in 2006. …

16: Ian J. Thompson

… ► 1953 in New Zealand) has been since 2006 a Theoretical Nuclear Physicist in the Nuclear Theory and Modeling Group of the Lawrence Livermore National Laboratory, Livermore, California. …

17: 28.36 Software

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Erricolo (2006). Fortran.

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18: 26.12 Plane Partitions

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Table 26.12.1: Plane partitions.

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$n$	$\mathrm{pp}\left(n\right)$	$n$	$\mathrm{pp}\left(n\right)$	$n$	$\mathrm{pp}\left(n\right)$
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11	859	28	24 83234	45	17740 79109
12	1479	29	37 59612	46	25435 35902
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14	4167	31	85 12309	48	51913 04973
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26.12.26 $$\mathrm{pp}\left(n\right)\sim \frac{{\left(\zeta \left(3\right)\right)}^{7/36}}{2^{11/36}{(3\pi )}^{1/2}{n}^{25/36}}\exp \left(3{\left(\zeta \left(3\right)\right)}^{1/3}{\left(\frac{1}{2}n\right)}^{2/3}+{\zeta }^{\prime }\left(-1\right)\right),$$

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Symbols:

$\zeta \left(s\right)$: Riemann zeta function, $\sim$: asymptotic equality, $\exp z$: exponential function, $\mathrm{pp}\left(n\right)$: number of plane partitions of $n$ , $n$: nonnegative integer and $\pi$: plane partition

Referenced by:

§26.12(iv), Erratum (V1.0.5) for Equation (26.12.26)

Permalink:

http://dlmf.nist.gov/26.12.E26

Encodings:

pMML, png, TeX

Errata (effective with 1.0.5):

The original statement of this equation, $\mathrm{pp}\left(n\right)\sim {\left(\frac{\zeta \left(3\right)}{2^{11}{n}^{25}}\right)}^{1/36}\exp \left(3{\left(\frac{\zeta \left(3\right)n^2}{4}\right)}^{1/3}+{\zeta }^{\prime }\left(-1\right)\right)$, has been corrected.

Reported 2011-09-05 by Suresh Govindarajan

See also:

Annotations for §26.12(iv), §26.12 and Ch.26

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19: Bibliography W

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Fast construction of the Fejér and Clenshaw-Curtis quadrature rules. BIT 46 (1), pp. 195–202.

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External Links:

ISSN 0006-3835, Document, MathReview Entry, ZentralBlatt

Referenced by:

§3.5(iv).

Encodings:

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Uniform asymptotics of the Stieltjes-Wigert polynomials via the Riemann-Hilbert approach. J. Math. Pures Appl. (9) 85 (5), pp. 698–718.

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External Links:

ISSN 0021-7824, Document, MathReview (Rabah Khaldi), ZentralBlatt

Referenced by:

§18.29.

Encodings:

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generatingfunctionology. 2nd edition, Academic Press Inc., Boston, MA.

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Notes:

A 3rd edition was published in 2006 by A.K. Peters, Ltd., Wellesley, MA.

External Links:

ISBN 0-12-751956-4, MathReview, ZentralBlatt

Referenced by:

§26.18, §26.7(i).

Encodings:

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Some hypergeometric orthogonal polynomials. SIAM J. Math. Anal. 11 (4), pp. 690–701.

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External Links:

ISSN 0036-1410, Document, MathReview (R. G. Buschman), ZentralBlatt

Referenced by:

§18.25(i), §18.25(i), §18.25(ii), §18.25(iii), §18.26(i), §18.26(ii), §18.38(iii).

Encodings:

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On the asymptotic behavior of the Fourier coefficients of Mathieu functions. J. Res. Nat. Inst. Standards Tech. 113 (1), pp. 11–15.

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External Links:

ISSN 1044-677X, FullText

Referenced by:

§28.4(vii).

Encodings:

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20: Bibliography C

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A moment problem and a family of integral evaluations. Trans. Amer. Math. Soc. 358 (9), pp. 4071–4097.

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External Links:

ISSN 0002-9947, Document, MathReview (Roelof Koekoek), ZentralBlatt

Referenced by:

§18.28(iv).

Encodings:

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The fourth Painlevé equation and associated special polynomials. J. Math. Phys. 44 (11), pp. 5350–5374.

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External Links:

ISSN 0022-2488, Document, MathReview, ZentralBlatt

Referenced by:

§32.8(iv).

Encodings:

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Painlevé Equations—Nonlinear Special Functions: Computation and Application. In Orthogonal Polynomials and Special Functions, F. Marcellàn and W. van Assche (Eds.), Lecture Notes in Math., Vol. 1883, pp. 331–411.

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External Links:

ISBN 3-540-31062-2, MathReview (Marta Mazzocco), ZentralBlatt

Referenced by:

Ch.32.

Encodings:

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Exact elliptic compactons in generalized Korteweg-de Vries equations. Complexity 11 (6), pp. 30–34.

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External Links:

ISSN 1076-2787, Document, MathReview

Referenced by:

§19.6(i).

Encodings:

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Chazy’s second-degree Painlevé equations. J. Phys. A 39 (39), pp. 11955–11971.

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External Links:

ISSN 0305-4470, Document, MathReview, ZentralBlatt

Referenced by:

§32.7(vii).

Encodings:

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