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21: 26.21 Tables

… ►Goldberg et al. (1976) contains tables of binomial coefficients to $n=100$ and Stirling numbers to $n=40$.

22: 26.9 Integer Partitions: Restricted Number and Part Size

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Table 26.9.1: Partitions $p_k\left(n\right)$.

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$n$	$k$
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8	0	1	5	10	15	18	20	21	22	22	22
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10	0	1	6	14	23	30	35	38	40	41	42

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23: 24.2 Definitions and Generating Functions

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Table 24.2.3: Bernoulli numbers $B_n=N/D$.

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$n$	$N$	$D$	$B_n$
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$20$	$-\mathrm{1\hspace{0.33em}74611}$	$330$	$-\mathrm{5.29124\hspace{0.33em}2424}$	$\mathrm{\times 10²}$
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$40$	$-\mathrm{2\hspace{0.33em}61082\hspace{0.33em}71849\hspace{0.33em}64491\hspace{0.33em}22051}$	$13530$	$-\mathrm{1.92965\hspace{0.33em}7934}$	$\mathrm{\times 10¹⁶}$
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Table 24.2.4: Euler numbers $E_n$.

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$n$	$E_n$
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$20$	$\mathrm{37037\hspace{0.33em}11882\hspace{0.33em}37525}$
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$40$	$\mathrm{1\hspace{0.33em}48511\hspace{0.33em}50718\hspace{0.33em}11498\hspace{0.33em}00178\hspace{0.33em}77156\hspace{0.33em}78140\hspace{0.33em}58266\hspace{0.33em}84425}$
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24: Bibliography S

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Transformations of the Jacobian amplitude function and its calculation via the arithmetic-geometric mean. SIAM J. Math. Anal. 20 (6), pp. 1514–1528.

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External Links:

ISSN 0036-1410, Document, MathReview (J. M. H. Peters), ZentralBlatt

Referenced by:

§22.19(i), §22.20(vi).

Encodings:

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The zeros of special functions from a fixed point method. SIAM J. Numer. Anal. 40 (1), pp. 114–133.

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External Links:

ISSN 1095-7170, Document, MathReview, ZentralBlatt

Referenced by:

§3.8(v).

Encodings:

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Uniform asymptotic forms of modified Mathieu functions. Quart. J. Mech. Appl. Math. 20 (3), pp. 365–380.

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External Links:

Document, MathReview (F. W. J. Olver), ZentralBlatt

Referenced by:

§28.8(iv).

Encodings:

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Prolate spheroidal wave functions, Fourier analysis and uncertainty. I. Bell System Tech. J. 40, pp. 43–63.

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External Links:

MathReview (I. Marx), ZentralBlatt

Referenced by:

§30.15(v).

Encodings:

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A Maple package for symmetric functions. J. Symbolic Comput. 20 (5-6), pp. 755–768.

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Notes:

For software see John Stembridge’s home page. The SF package contains Maple software for zonal, Jack, and Macdonald polynomials.

External Links:

Home Page, ISSN 0747-7171, Document, MathReview, ZentralBlatt

Referenced by:

3rd item.

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25: Bibliography C

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Some series and bounds for incomplete elliptic integrals. J. Math. and Phys. 40, pp. 125–134.

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External Links:

MathReview (L. Robin), ZentralBlatt

Referenced by:

§19.15, (19.5.1), (19.5.2), (19.5.4), (19.5.4_1), (19.5.4_2), (19.5.4_3), §19.9(ii).

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Asymptotic estimates for generalized Stirling numbers. Analysis (Munich) 20 (1), pp. 1–13.

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External Links:

ISSN 0174-4747, MathReview (F. T. Howard), ZentralBlatt

Referenced by:

§26.8(vii).

Encodings:

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Chebyshev expansions for the Bessel function $J_n(z)$ in the complex plane. Math. Comp. 40 (161), pp. 343–366.

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External Links:

ISSN 0025-5718, FullText, MathReview (C. W. Clenshaw), ZentralBlatt

Referenced by:

§10.76(ii).

Encodings:

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Validated computation of certain hypergeometric functions. ACM Trans. Math. Software 38 (2), pp. Art. 11, 20.

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External Links:

ISSN 0098-3500, Document, FullText, MathReview Entry, ZentralBlatt

Referenced by:

§13.29(v), §15.19(v).

Encodings:

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Coulomb effects in the Klein-Gordon equation for pions. Phys. Rev. C 20 (2), pp. 696–704.

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External Links:

Document

Referenced by:

5th item.

Encodings:

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26: Bibliography W

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The Nahm equations, finite-gap potentials and Lamé functions. J. Phys. A 20 (10), pp. 2679–2683.

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External Links:

ISSN 0305-4470, Document, MathReview (James M. D’Archangelo), ZentralBlatt

Referenced by:

§29.19(ii).

Encodings:

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Harmonic Analysis. In Studies in Real and Complex Analysis, I. I. Hirschman (Ed.), Studies in Mathematics, Vol. 3, pp. 124–178.

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External Links:

MathReview, ZentralBlatt

Referenced by:

§1.15(iii), §1.15(iv), §1.15(v).

Encodings:

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Asymptotic Approximations to Truncation Errors of Series Representations for Special Functions. In Algorithms for Approximation, A. Iske and J. Levesley (Eds.), pp. 331–348.

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External Links:

ISBN 3-540-33283-9, Document, MathReview Entry, ZentralBlatt

Referenced by:

§2.10(i).

Encodings:

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Group Theory and its Application to the Quantum Mechanics of Atomic Spectra. Pure and Applied Physics. Vol. 5, Academic Press, New York.

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Notes:

Expanded and improved ed. Translated from the German by J. J. Griffin.

External Links:

ISBN 0-12-750550-4, MathReview (A. S. Wightman), ZentralBlatt

Referenced by:

§34.12.

Encodings:

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A class of integral transforms. Proc. Edinburgh Math. Soc. (2) 14, pp. 33–40.

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External Links:

Document, MathReview (B. R. Bhonsle), ZentralBlatt

Referenced by:

§13.23(iv).

Encodings:

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27: Bibliography M

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Orthogonal polynomials associated with root systems. Sém. Lothar. Combin. 45, pp. Art. B45a, 40 pp. (electronic).

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External Links:

ISSN 1286-4889, FullText, MathReview, ZentralBlatt

Referenced by:

§18.37(iii).

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Rational approximations, software and test methods for sine and cosine integrals. Numer. Algorithms 12 (3-4), pp. 259–272.

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Notes:

Includes Fortran code, maximum accuracy 20S.

External Links:

ISSN 1017-1398, Document, MathReview, ZentralBlatt

Referenced by:

§6.13, 4th item, §6.21(ii).

Encodings:

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Calculation of the modified Bessel functions of the second kind with complex argument. Math. Comp. 20 (95), pp. 407–412.

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External Links:

ISSN 0025-5718, FullText, MathReview (H. E. Fettis), ZentralBlatt

Referenced by:

§10.74(iii).

Encodings:

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Hierarchies and logarithmic oscillations in the temporal relaxation patterns of proteins and other complex systems. Proc. Nat. Acad. Sci. U .S. A. 96 (20), pp. 11085–11089.

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External Links:

FullText

Referenced by:

§8.24(i).

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The $q$-analogue of the Laguerre polynomials. J. Math. Anal. Appl. 81 (1), pp. 20–47.

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External Links:

ISSN 0022-247X, Document, MathReview (R. A. Askey), ZentralBlatt

Referenced by:

§18.27(v).

Encodings:

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28: Bibliography L

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Algorithm 917: complex double-precision evaluation of the Wright $\omega$ function. ACM Trans. Math. Software 38 (3), pp. Art. 20, 17.

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External Links:

ISSN 0098-3500, Document, FullText, MathReview Entry, ZentralBlatt

Referenced by:

§4.13, 2nd item, §4.48(iv).

Encodings:

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An asymptotic estimate for the Bernoulli and Euler numbers. Canad. Math. Bull. 20 (1), pp. 109–111.

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External Links:

MathReview (D. H. Lehmer), ZentralBlatt

Referenced by:

§24.11.

Encodings:

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Inequalities for ultraspherical polynomials and the gamma function. J. Approx. Theory 40 (2), pp. 115–120.

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External Links:

ISSN 0021-9045, Document, MathReview (B. R. Bhonsle), ZentralBlatt

Referenced by:

§18.14(i).

Encodings:

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Combinatorics in Pure Mathematics. In Handbook of Combinatorics, Vol. 2, R. L. Graham, M. Grötschel, and L. Lovász (Eds.), pp. 2039–2082.

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External Links:

MathReview, ZentralBlatt

Referenced by:

§26.19.

Encodings:

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An underflow-induced graphics failure solved by SLI arithmetic. In IEEE Symposium on Computer Arithmetic, E. E. Swartzlander, M. J. Irwin, and G. A. Jullien (Eds.), Washington, D.C., pp. 10–17.

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External Links:

FullText

Referenced by:

§3.1(iv).

Encodings:

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29: Foreword

… ► The success of the original handbook, widely referred to as “Abramowitz and Stegun” (“A&S”), derived not only from the fact that it provided critically useful scientific data in a highly accessible format, but also because it served to standardize definitions and notations for special functions. … ►November 20, 2009 …

30: 20.3 Graphics

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Figure 20.3.6: ${\theta }_1(x,q)$, $0\le q\le 1$, $x$ = 0, 0. 4, 5, 10, 40. Magnify

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Figure 20.3.7: ${\theta }_2(x,q)$, $0\le q\le 1$, $x$ = 0, 0. 4, 5, 10, 40. Magnify

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Figure 20.3.8: ${\theta }_3(x,q)$, $0\le q\le 1$, $x$ = 0, 0. 4, 5, 10, 40. Magnify

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Figure 20.3.9: ${\theta }_4(x,q)$, $0\le q\le 1$, $x$ = 0, 0. 4, 5, 10, 40. Magnify

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