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11: 26.21 Tables

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

12: 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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Landen Transformations of Integrals. In Asymptotic and Computational Analysis (Winnipeg, MB, 1989), R. Wong (Ed.), Lecture Notes in Pure and Appl. Math., Vol. 124, pp. 75–94.

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External Links:

MathReview, ZentralBlatt

Referenced by:

§19.22(iii).

Encodings:

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A Unified Approach to Recurrence Algorithms. In Approximation and Computation (West Lafayette, IN, 1993), R. V. M. Zahar (Ed.), International Series of Computational Mathematics, Vol. 119, pp. 97–120.

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External Links:

ISBN 0-8176-3753-2, MathReview (R. M. M. Mattheij), ZentralBlatt

Referenced by:

§3.6(vii).

Encodings:

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On Stieltjes’ continued fraction for the gamma function. Math. Comp. 34 (150), pp. 547–551.

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External Links:

ISSN 0025-5718, FullText, MathReview, ZentralBlatt

Referenced by:

§5.10.

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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13: Bibliography L

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The real zeros of the Bernoulli polynomials. J. Approx. Theory 58 (2), pp. 124–150.

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External Links:

ISSN 0021-9045, Document, MathReview (Boro Döring), ZentralBlatt

Referenced by:

§24.12(i), §24.9.

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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Airy and Bessel Functions by Parallel Integration of ODEs. In Proceedings of the Sixth SIAM Conference on Parallel Processing for Scientific Computing, R. F. Sincovec, D. E. Keyes, M. R. Leuze, L. R. Petzold, and D. A. Reed (Eds.), Philadelphia, PA, pp. 530–538.

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External Links:

ISBN 0-89871-315-3

Referenced by:

§10.74(ii), §3.7(iii), §9.17(ii).

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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14: Bibliography S

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Quantum Chaos, Symmetry and Zeta Functions. Lecture I, Quantum Chaos. In Current Developments in Mathematics, 1997 (Cambridge, MA), R. Bott (Ed.), pp. 127–144.

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External Links:

MathReview (Shin-ya Koyama), ZentralBlatt

Referenced by:

§25.17.

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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The Gaussian Function in Calculations of Statistical Mechanics and Quantum Mechanics. In Methods in Computational Physics: Advances in Research and Applications, B. Alder, S. Fernbach, and M. Rotenberg (Eds.), Vol. 2, pp. 1–45.

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Referenced by:

§8.24(i), §8.24(iii).

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 stable quotient-difference algorithm. Math. Comp. 34 (150), pp. 515–519.

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External Links:

ISSN 0025-5718, FullText, MathReview, ZentralBlatt

Referenced by:

§3.10(ii).

Encodings:

BibTeX

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15: Bibliography R

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Algorithm 935: IIPBF, a MATLAB toolbox for infinite integral of products of two Bessel functions. ACM Trans. Math. Softw. 40 (2), pp. 14:1–14:12.

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External Links:

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

Referenced by:

§10.74(vii), §10.74(vii), 7th item, §10.77(ix).

Encodings:

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Hypergeometric Functions on Domains of Positivity, Jack Polynomials, and Applications. Contemporary Mathematics, Vol. 138, American Mathematical Society, Providence, RI.

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External Links:

ISBN 0-8218-5159-4, MathReview, ZentralBlatt

Referenced by:

Ch.35, Profile Donald St. P. Richards.

Encodings:

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Heun’s Differential Equations. The Clarendon Press Oxford University Press, New York.

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External Links:

ISBN 0-19-859695-2, MathReview (Harold Exton), ZentralBlatt

Referenced by:

§31.1, §31.12, §31.13, §31.2(v), §31.2(i), §31.2(iv), §31.3(ii), §31.4, §31.7(ii), §31.9(i), Ch.31, Profile Gerhard Wolf.

Encodings:

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Another proof of the triple sum formula for Wigner $9j$-symbols. J. Math. Phys. 40 (12), pp. 6689–6691.

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External Links:

ISSN 0022-2488, Document, MathReview (Michael Wüstner), ZentralBlatt

Referenced by:

§34.6.

Encodings:

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Combinatorics in Chemistry. In Handbook of Combinatorics, Vol. 2, R. L. Graham, M. Grötschel, and L. Lovász (Eds.), pp. 1955–1981.

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External Links:

MathReview (Haruo Hosoya), ZentralBlatt

Referenced by:

§26.20.

Encodings:

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16: 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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17: 25.3 Graphics

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Figure 25.3.3: Modulus of the Riemann zeta function $|\zeta \left(x+\mathrm{i}y\right)|$, $-4\le x\le 4$, $-10\le y\le 40$. Magnify 3D Help

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18: Bibliography P

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Tables of Digamma and Trigamma Functions. In Tracts for Computers, No. 1, K. Pearson (Ed.),

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External Links:

ZentralBlatt

Referenced by:

§5.1, Notations F.

Encodings:

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Zonal Polynomials of Order $1$ Through $12$ . In Selected Tables in Mathematical Statistics, H. L. Harter and D. B. Owen (Eds.), Vol. 2, pp. 199–388.

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External Links:

MathReview

Referenced by:

§35.11.

Encodings:

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Handbook of the Normal Distribution. Statistics: Textbooks and Monographs, Vol. 40, Marcel Dekker Inc., New York.

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Notes:

A revised and expanded 2nd edition was published in 1996.

External Links:

ISBN 0-8247-1541-1, MathReview (S. Kotz), ZentralBlatt

Referenced by:

§7.20(iii).

Encodings:

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Tables of the Incomplete Beta-function. 2nd edition, Published for the Biometrika Trustees at the Cambridge University Press, Cambridge.

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External Links:

MathReview, ZentralBlatt

Referenced by:

1st item.

Encodings:

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Voronoi type congruences for Bernoulli numbers. In Voronoi’s Impact on Modern Science. Book I, P. Engel and H. Syta (Eds.),

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External Links:

ZentralBlatt

Referenced by:

§24.10(iii).

Encodings:

BibTeX

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19: Bibliography O

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Asymptotic Enumeration Methods. In Handbook of Combinatorics, Vol. 2, L. Lovász, R. L. Graham, and M. Grötschel (Eds.), pp. 1063–1229.

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External Links:

ISBN 0-444-82351-4, Pdf, MathReview (Konrad Engel), ZentralBlatt

Referenced by:

Ch.2.

Encodings:

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On the asymptotic and numerical solution of linear ordinary differential equations. SIAM Rev. 40 (3), pp. 463–495.

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External Links:

ISSN 1095-7200, Document, MathReview (W. Balser), ZentralBlatt

Referenced by:

§16.25, §2.7(ii), §3.7(iii).

Encodings:

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Bessel Functions. Part III: Zeros and Associated Values. Royal Society Mathematical Tables, Volume 7, Cambridge University Press, Cambridge-New York.

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External Links:

ISBN 0-521-06153-9, MathReview (L. Fox), ZentralBlatt

Referenced by:

§10.21(vi), §10.21(viii), §10.58, §10.74(vi), 1st item, 2nd item.

Encodings:

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Error Analysis of Complex Arithmetic. In Computational Aspects of Complex Analysis (Braunlage, 1982), H. Werner, L. Wuytack, E. Ng, and H. J. Bünger (Eds.), NATO Adv. Sci. Inst. Ser. C: Math. Phys. Sci., Vol. 102, pp. 279–292.

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External Links:

MathReview (G. Blanch), ZentralBlatt

Referenced by:

§3.1(v).

Encodings:

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The Generalized Exponential Integral. In Approximation and Computation (West Lafayette, IN, 1993), R. V. M. Zahar (Ed.), International Series of Numerical Mathematics, Vol. 119, pp. 497–510.

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External Links:

MathReview (Richard B. Paris), ZentralBlatt

Referenced by:

§2.11(iii), §8.19(viii).

Encodings:

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20: 6.6 Power Series

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