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11: Vadim B. Kuznetsov

… ►He was also editor of The Kowalevski Property, CRM Proceedings and Lecture Notes 32, published by the American Mathematical Society in 2002. …

12: 30.9 Asymptotic Approximations and Expansions

… ►

2^{6}\beta_{1}=-q^{3}-11q+32m^{2}q,

… ►

2^{20}\beta_{5}=-527q^{7}-61529q^{5}-10\;43961q^{3}-22\;41599q+32m^{2}(5739q^{% 5}+1\;27550q^{3}+2\;98951q)-2048m^{4}(355q^{3}+1505q)+65536m^{6}q.

… ►

2^{9}c_{3}=-33q^{5}-114q^{3}-37q+2m^{2}(23q^{3}+25q)-13m^{4}q.

…

13: 26.10 Integer Partitions: Other Restrictions

… ►

Table 26.10.1: Partitions restricted by difference conditions, or equivalently with parts from

A_{j,k}

► ►►►►►

	$p\left(\mathcal{D},n\right)$	$p\left(\mathcal{D}2,n\right)$	$p\left(\mathcal{D}2,\hbox{}\!\!\in\!T,n\right)$	$p\left(\mathcal{D}^{\prime}3,n\right)$
…
$9$	$8$	$5$	$3$	$3$
…
$15$	$27$	$14$	$9$	$9$
$16$	$32$	$17$	$11$	$10$
…

► … ►Note that

p\left(\mathcal{D}^{\prime}3,n\right)\leq p\left(\mathcal{D}3,n\right)

, with strict inequality for

n\geq 9

. It is known that for

k>3

p\left(\mathcal{D}k,n\right)\geq p\left(\in\!A_{1,k+3},n\right)

, with strict inequality for

n

sufficiently large, provided that

k=2^{m}-1,m=3,4,5

, or

k\geq 32

; see Yee (2004). …

14: Bibliography G

… ►

G. Gasper (1972) An inequality of Turán type for Jacobi polynomials. Proc. Amer. Math. Soc. 32, pp. 435–439.

ⓘ

External Links:: ISSN 0002-9939, Document, MathReview (A. E. Danese), ZentralBlatt
Referenced by:: §18.14(ii).
Encodings:: BibTeX

… ►

W. Gautschi and J. Slavik (1978) On the computation of modified Bessel function ratios. Math. Comp. 32 (143), pp. 865–875.

ⓘ

External Links:: ISSN 0025-5718, FullText, MathReview (James M. Horner), ZentralBlatt
Referenced by:: §10.74(v).
Encodings:: BibTeX

… ►

A. Gil, J. Segura, and N. M. Temme (2006a) Computing the real parabolic cylinder functions

U(a,x)

V(a,x)

. ACM Trans. Math. Software 32 (1), pp. 70–101.

ⓘ

External Links:: ISSN 0098-3500, Document, MathReview (Syamal K. Sen), ZentralBlatt
Referenced by:: §12.18.
Encodings:: BibTeX

… ►

J. N. Ginocchio (1991) A new identity for some six-

j

symbols. J. Math. Phys. 32 (6), pp. 1430–1432.

ⓘ

External Links:: ISSN 0022-2488, Document, MathReview
Referenced by:: §34.5(vi).
Encodings:: BibTeX

… ►

A. Gray, G. B. Mathews, and T. M. MacRobert (1922) A Treatise on Bessel Functions and their Applications to Physics. 2nd edition, Macmillan and Co., London.

ⓘ

Notes:: Table errata: Math. Comp. v. 24 (1970), p. 240, v. 31 (1978), pp. 806 and 1046, and v. 32 (1978), pp. 318. Reprinted by Dover Publications Inc., New York, 1966.
External Links:: MathReview, ZentralBlatt
Referenced by:: §10.21(x), §10.73(i), §10.73(i).
Encodings:: BibTeX

…

15: 34.12 Physical Applications

§34.12 Physical Applications

►The angular momentum coupling coefficients (

\mathit{3j}

\mathit{6j}

, and

\mathit{9j}

symbols) are essential in the fields of nuclear, atomic, and molecular physics. …

\mathit{3j},\mathit{6j}

, and

\mathit{9j}

symbols are also found in multipole expansions of solutions of the Laplace and Helmholtz equations; see Carlson and Rushbrooke (1950) and Judd (1976).

16: Bibliography Z

… ►

M. R. Zaghloul (2016) Remark on “Algorithm 916: computing the Faddeyeva and Voigt functions”: efficiency improvements and Fortran translation. ACM Trans. Math. Softw. 42 (3), pp. 26:1–26:9.

ⓘ

Notes:: Includes MATLAB and Fortran programs claiming 6S or 13S accuracy for single and double precision
External Links:: ISSN 0098-3500, Link, Document, MathReview Entry
Referenced by:: 3rd item, 6th item, §7.25(iii), §7.25(vi).
Encodings:: BibTeX

►

M. R. Zaghloul (2017) Algorithm 985: Simple, Efficient, and Relatively Accurate Approximation for the Evaluation of the Faddeyeva Function. ACM Trans. Math. Softw. 44 (2), pp. 22:1–22:9.

ⓘ

External Links:: ISSN 0098-3500, Link, Document, MathReview Entry, ZentralBlatt
Referenced by:: 4th item, §7.25(iii).
Encodings:: BibTeX

… ►

R. Zanovello (1975) Sul calcolo numerico della funzione di Struve

\mathbf{H}_{\nu}(z)

. Rend. Sem. Mat. Univ. e Politec. Torino 32, pp. 251–269 (Italian. English summary).

ⓘ

External Links:: MathReview (Walter Gautschi), ZentralBlatt
Referenced by:: §11.13(i), 4th item.
Encodings:: BibTeX

… ►

J. Zhang (1996) A note on the

\tau

-method approximations for the Bessel functions

Y_{0}(z)

and

Y_{1}(z)

. Comput. Math. Appl. 31 (9), pp. 63–70.

ⓘ

External Links:: ISSN 0898-1221, Document, MathReview, ZentralBlatt
Referenced by:: §10.76(ii).
Encodings:: BibTeX

…

17: Peter A. Clarkson

… ►

32 Painlevé Transcendents

…

18: Bibliography W

… ►

S. S. Wagstaff (1978) The irregular primes to

125000

. Math. Comp. 32 (142), pp. 583–591.

ⓘ

External Links:: FullText, Document, MathReview (Wells Johnson), ZentralBlatt
Referenced by:: §24.20.
Encodings:: BibTeX

… ►

J. K. G. Watson (1999) Asymptotic approximations for certain

6

j

and

9

j

symbols. J. Phys. A 32 (39), pp. 6901–6902.

ⓘ

External Links:: ISSN 0305-4470, Document, MathReview, ZentralBlatt
Referenced by:: §34.8, §34.8.
Encodings:: BibTeX

►

J. V. Wehausen and E. V. Laitone (1960) Surface Waves. In Handbuch der Physik, Vol. 9, Part 3, pp. 446–778.

ⓘ

External Links:: Online edition, MathReview (F. Ursell), ZentralBlatt
Referenced by:: §11.12.
Encodings:: BibTeX

… ►

J. Wishart (1928) The generalised product moment distribution in samples from a normal multivariate population. Biometrika 20A, pp. 32–52.

ⓘ

External Links:: FullText, Document, ZentralBlatt
Referenced by:: §35.3(i), §35.3(ii).
Encodings:: BibTeX

… ►

F. J. Wright (1980) The Stokes set of the cusp diffraction catastrophe. J. Phys. A 13 (9), pp. 2913–2928.

ⓘ

External Links:: ISSN 0305-4470, Document, MathReview (I. Stewart), ZentralBlatt
Referenced by:: §36.5(ii).
Encodings:: BibTeX

…

19: 24.2 Definitions and Generating Functions

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Table 24.2.3: Bernoulli numbers

B_{n}=N/D

► ►►►

$n$	$N$	$D$	$B_{n}$
…
$32$	$-770\;93210\;41217$	$510$	$-1.51163\;1577$	$\times 10^{10}$
…

► ►

Table 24.2.4: Euler numbers

E_{n}

► ►►►

$n$	$E_{n}$
…
$32$	$17751\;93915\;79539\;28943\;66647\;89665$
…

► ►

Table 24.2.5: Coefficients

b_{n,k}

of the Bernoulli polynomials

B_{n}\left(x\right)=\sum_{k=0}^{n}b_{n,k}x^{k}

► ►►►►

	$k$
$n$	$0$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$	$12$	$13$	$14$	$15$
…
$9$	$0$	$-\tfrac{3}{10}$	$0$	$2$	$0$	$-\tfrac{21}{5}$	$0$	$6$	$-\tfrac{9}{2}$	$1$
…

► ►

Table 24.2.6: Coefficients

e_{n,k}

of the Euler polynomials

E_{n}\left(x\right)=\sum_{k=0}^{n}e_{n,k}x^{k}

► ►►►

	$k$
…
$9$	$-\tfrac{31}{2}$	$0$	$\tfrac{153}{2}$	$0$	$-63$	$0$	$21$	$0$	$-\tfrac{9}{2}$	$1$
…

►

20: 9 Airy and Related Functions

Chapter 9 Airy and Related Functions

…