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1: 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).

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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).

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The real roots of Bernoulli polynomials. Ann. Univ. Turku. Ser. A I 37, pp. 1–20.

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External Links:

MathReview (D. H. Lehmer), ZentralBlatt

Referenced by:

§24.12(i).

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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).

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A First Course in the Numerical Analysis of Differential Equations. Cambridge Texts in Applied Mathematics, No. 15, Cambridge University Press, Cambridge.

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External Links:

ISBN 0-521-55376-8; 0-521-55655-4, MathReview (Luis Verde-Star), ZentralBlatt

Referenced by:

§3.7(i).

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2: Publications

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Using Numerical Grid Generation to Facilitate 3D Visualization of Complicated Mathematical Functions, Technical Report NISTIR 6413 (November 1999), National Institute of Standards and Technology.

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From 2D to 3D: Numerical Grid Generation and the Visualization of Complex Surfaces, Proceedings of the 7th International Conference on Numerical Grid Generation in Computational Field Simulations, Whistler, British Columbia, Canada, September 25-28, 2000.

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Web-Based 3D Visualization in a Digital Library of Mathematical Functions, Proceedings of the Web3D Symposium, Bangor, UK, March 29–April 1, 2005.

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From B-Spline Mesh Generation to Effective Visualizations for the NIST Digital Library of Mathematical Functions, in Curve and Surface Design, Proceedings of the Sixth International Conference on Curves and Surfaces, Avignon, France June 29–July 5, 2006, pp. 235–243.

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NIST’s Digital Library of Mathematial Functions, Physics Today 71, 2, 48 (2018), pp. 48–53.

3: Bibliography K

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An indirect method for evaluating certain infinite integrals. Z. Angew. Math. Phys. 29 (3), pp. 380–386.

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External Links:

ISSN 0044-2275, Document, MathReview, ZentralBlatt

Referenced by:

§10.71(ii).

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An adaptive contour code for the numerical evaluation of the oscillatory cuspoid canonical integrals and their derivatives. Computer Physics Comm. 132 (1-2), pp. 142–165.

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External Links:

Document, Code, ZentralBlatt

Referenced by:

§36.15(iii).

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Comment on “The incomplete beta function law for parallel tempering sampling of classical canonical systems” [J. Chem. Phys. 120, 4119 (2004)]. J. Chem. Phys. 121 (2), pp. 1167.

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External Links:

Document

Referenced by:

§8.24(ii).

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Clebsch-Gordan coefficients for $\mathrm{SU}(2)$ and Hahn polynomials. Nieuw Arch. Wisk. (3) 29 (2), pp. 140–155.

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External Links:

ISSN 0028-9825, MathReview (Jiří Patera), ZentralBlatt

Referenced by:

§18.38(iii).

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Zeros of exceptional Hermite polynomials. J. Approx. Theory 200, pp. 28–39.

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External Links:

ISSN 0021-9045, Document, Link, MathReview (Mario Pérez Riera)

Referenced by:

§18.39(i).

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4: Bibliography S

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Numerical evaluation of the Hankel transform. Comput. Phys. Comm. 116 (2-3), pp. 278–294.

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External Links:

ISSN 0010-4655, Document, MathReview Entry, ZentralBlatt

Referenced by:

§10.74(vii).

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The elliptical microstrip antenna with circular polarization. IEEE Trans. Antennas and Propagation 29 (1), pp. 90–94.

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External Links:

FullText

Referenced by:

5th item.

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Sturm oscillation and comparison theorems. In Sturm-Liouville theory, pp. 29–43.

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External Links:

Document, Link, MathReview Entry

Referenced by:

§18.36(vi), §18.39(i).

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On numerical Bessel transformation. Comput. Phys. Comm. 16 (3), pp. 383–387.

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Notes:

Single-precision Fortran, maximum accuracy 15D.

External Links:

ISSN 0010-4655, Document, Code

Referenced by:

8th item.

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Numerical Methods Based on Sinc and Analytic Functions. Springer Series in Computational Mathematics, Vol. 20, Springer-Verlag, New York.

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Notes:

Sinc-Pack, a set of 480 Matlab programs with a 470-page tutorial, is available for purchase from SINC, LLC by contacting Frank Stenger.

External Links:

ISBN 0-387-94008-1, MathReview (B. Boyanov), ZentralBlatt

Referenced by:

§3.3(vi), §3.4(i), §3.5(i).

Encodings:

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5: Bibliography M

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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).

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Numerical Methods for Roots of Polynomials. Part I. Studies in Computational Mathematics, Vol. 14, Elsevier, Amsterdam.

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External Links:

ISBN 978-0-444-52729-5; 0-444-52729-X, MathReview Entry, ZentralBlatt

Referenced by:

§3.8(iv).

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Calculation of the complete elliptic integrals with complex modulus. Numer. Math. 29 (2), pp. 233–236.

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Notes:

An Algol procedure for calculating the complete elliptic integrals of the first and the second kind with complex modulus $k$ is included.

External Links:

ISSN 0029-599X, Document, MathReview (H. E. Fettis), ZentralBlatt

Referenced by:

§19.36(ii), §19.39(ii).

Encodings:

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Stirling numbers of the second kind. Duke Math. J. 25 (1), pp. 29–43.

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External Links:

Document, MathReview (A. Sade), ZentralBlatt

Referenced by:

§26.1, §26.8(vii), Notations S.

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Rational solutions of the second and the fourth Painlevé equations. Funkcial. Ekvac. 28 (1), pp. 1–32.

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External Links:

ISSN 0532-8721, FullText, MathReview (Hélène Airault), ZentralBlatt

Referenced by:

§32.8(iv).

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6: Bibliography L

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Asymptotic and numeric study of eigenvalues of the double confluent Heun equation. J. Phys. A 31 (42), pp. 8521–8531.

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ISSN 0305-4470, Document, MathReview, ZentralBlatt

Referenced by:

§31.13, §31.18.

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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.

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Eine Verallgemeinerung der Sphäroidfunktionen. Arch. Math. 11, pp. 29–39.

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ISSN 0003-9268, Document, MathReview (M. J. O. Strutt), ZentralBlatt

Referenced by:

§30.12.

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Lie algebraic approaches to classical partition identities. Adv. in Math. 29 (1), pp. 15–59.

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ISSN 0001-8708, Document, MathReview (S. I. Gel’fand), ZentralBlatt

Referenced by:

§17.16.

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Asymptotics and numerics of polynomials used in Tricomi and Buchholz expansions of Kummer functions. Numer. Math. 116 (2), pp. 269–289.

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External Links:

ISSN 0029-599X, Document, FullText, MathReview (Richard B. Paris), ZentralBlatt

Referenced by:

§13.11, §13.11.

Encodings:

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7: Bibliography B

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Algorithms for computing Bessel functions of half-integer order with complex arguments. Zh. Vychisl. Mat. i Mat. Fiz. 28 (10), pp. 1449–1460, 1597.

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Notes:

English translation in U.S.S.R. Comput. Math. and Math. Phys. 28(1988), no. 5, 109–117

External Links:

ISSN 0044-4669, Document, MathReview (Walter Gautschi), ZentralBlatt

Referenced by:

§10.77(iv).

Encodings:

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Algorithms for evaluating spherical Bessel functions in the complex domain. Zh. Vychisl. Mat. i Mat. Fiz. 28 (12), pp. 1779–1788, 1918.

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Notes:

English translation in U.S.S.R. Comput. Math. and Math. Phys. 28(1988), no. 6, 122–128

External Links:

ISSN 0044-4669, Document, MathReview (Walter Gautschi), ZentralBlatt

Referenced by:

§10.77(iv).

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Products of generalized hypergeometric series. Proc. London Math. Soc. (2) 28 (2), pp. 242–254.

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External Links:

Document, ZentralBlatt

Referenced by:

§16.12.

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Transformations of generalized hypergeometric series. Proc. London Math. Soc. (2) 29 (2), pp. 495–502.

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External Links:

Document, ZentralBlatt

Referenced by:

§16.6.

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Über Sturm-Liouvillesche Polynomsysteme. Math. Z. 29 (1), pp. 730–736.

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External Links:

ISSN 0025-5874, Link, MathReview Entry, ZentralBlatt

Referenced by:

item 1..

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8: Bibliography O

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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).

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Hyperasymptotic solutions of higher order linear differential equations with a singularity of rank one. Proc. Roy. Soc. London Ser. A 454, pp. 1–29.

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ISSN 1364-5021, Document, MathReview (Donald A. Lutz), ZentralBlatt

Referenced by:

§2.11(v), §2.7(ii).

Encodings:

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Error bounds for stationary phase approximations. SIAM J. Math. Anal. 5 (1), pp. 19–29.

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Notes:

See also Olver (1997b)

External Links:

Document, MathReview (L. Berg), ZentralBlatt

Referenced by:

§2.3(iv).

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Numerical solution of Riemann-Hilbert problems: Painlevé II. Found. Comput. Math. 11 (2), pp. 153–179.

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External Links:

ISSN 1615-3375, Document, FullText, MathReview Entry, ZentralBlatt

Referenced by:

§32.17, §32.17.

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Modified quotients of cylinder functions. Math. Tables Aids Comput. 10, pp. 27–28.

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External Links:

ISSN 0891-6837, MathReview Entry, ZentralBlatt

Referenced by:

§10.29(i), §10.6(i).

Encodings:

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9: 26.4 Lattice Paths: Multinomial Coefficients and Set Partitions

… ►Table 26.4.1 gives numerical values of multinomials and partitions $\lambda ,M_1,M_2,M_3$ for $1\le m\le n\le 5$. … ►

Table 26.4.1: Multinomials and partitions.

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$n$	$m$	$\lambda$	$M_1$	$M_2$	$M_3$
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$5$	$2$	$2^1,3^1$	$10$	$20$	$10$
$5$	$3$	$1^2,3^1$	$20$	$20$	$10$
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10: Bibliography F

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Sur certaines sommes des intégral-cosinus. Bull. Soc. Math. Phys. Serbie 12, pp. 13–20 (French).

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External Links:

MathReview (L. Carlitz), ZentralBlatt

Referenced by:

§6.15.

Encodings:

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Numerical calculation of singular integrals related to Hankel transform. Comput. Math. Appl. 21 (2-3), pp. 87–94.

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Notes:

Fortran, minimum precision 6D.

External Links:

ISSN 0898-1221, Document, MathReview, ZentralBlatt

Referenced by:

§10.77(ix).

Encodings:

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Application of the $\tau$-function theory of Painlevé equations to random matrices: ${\mathrm{P}}_{\mathrm{VI}}$, the JUE, CyUE, cJUE and scaled limits. Nagoya Math. J. 174, pp. 29–114.

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External Links:

ISSN 0027-7630, MathReview, ZentralBlatt

Referenced by:

§32.10(vi), §32.6(v).

Encodings:

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Numerical evaluation of the elliptic integral of the third kind. Math. Comp. 19 (91), pp. 494–496.

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External Links:

FullText, MathReview, ZentralBlatt

Referenced by:

§19.36(iv).

Encodings:

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Numerical treatment of Coulomb wave functions. Rev. Mod. Phys. 27 (4), pp. 399–411.

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External Links:

Document, MathReview (A. Erdélyi), ZentralBlatt

Referenced by:

§33.10(ii), §33.11, §33.12(i), §33.9(ii).

Encodings:

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