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11: Bibliography F

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Polynomial relations in the Heisenberg algebra. J. Math. Phys. 35 (11), pp. 6144–6149.

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External Links:

ISSN 0022-2488, Document, MathReview (Shao-Ming Fei), ZentralBlatt

Referenced by:

§13.3(ii), §15.5(i), §16.3(i).

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Transverse cusp diffraction catastrophes produced by the reflection of ultrasonic tone bursts from a curved surface in water. J. Acoust. Soc. Amer. 92 (5), pp. 2869–2877.

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External Links:

Document

Referenced by:

§36.14(iv).

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Travel time surface of a transverse cusp caustic produced by reflection of acoustical transients from a curved metal surface. J. Acoust. Soc. Amer. 95 (2), pp. 650–660.

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External Links:

Document

Referenced by:

§36.14(iv).

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Algebraic methods to compute Mathieu functions. J. Phys. A 34 (17), pp. 3541–3551.

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External Links:

ISSN 0305-4470, Document, Link, MathReview (Aleksander Denisiuk), ZentralBlatt

Referenced by:

§28.6(i), §28.6(i), §28.6(ii), §28.6(ii), §28.8(i), §28.8(i), §28.8(ii), §28.8(ii), Erratum (V1.1.10) for Sections 28.6(i), 28.6(ii), 28.8(i), 28.8(ii).

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12: Bibliography K

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Introduction to Elliptic Curves and Modular Forms. 2nd edition, Graduate Texts in Mathematics, Vol. 97, Springer-Verlag, New York.

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External Links:

ISBN 0-387-97966-2, MathReview, ZentralBlatt

Referenced by:

§20.10(i), §20.12(i), §20.9(iii), §22.18(iv), §23.1, §23.20(ii), §23.20(v), Ch.23.

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Algebraic Aspects of Cryptography. Springer-Verlag, Berlin.

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Notes:

Second printing with corrections

External Links:

ISBN 3-540-63446-0, MathReview (M. V. D. Burmester), ZentralBlatt

Referenced by:

§23.20(iii).

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Orthogonal polynomials and computer algebra. In Recent developments in complex analysis and computer algebra (Newark, DE, 1997), R. P. Gilbert, J. Kajiwara, and Y. S. Xu (Eds.), Int. Soc. Anal. Appl. Comput., Vol. 4, Dordrecht, pp. 205–234.

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External Links:

FullText, MathReview Entry, ZentralBlatt

Referenced by:

CAOP (website).

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Meixner-Pollaczek polynomials and the Heisenberg algebra. J. Math. Phys. 30 (4), pp. 767–769.

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External Links:

ISSN 0022-2488, Document, MathReview, ZentralBlatt

Referenced by:

§18.21(ii).

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The relationship between Zhedanov’s algebra $\mathrm{AW}(3)$ and the double affine Hecke algebra in the rank one case. SIGMA 3, pp. Paper 063, 15 pp..

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External Links:

ISSN 1815-0659, Link, MathReview (James W. Parkinson), ZentralBlatt

Referenced by:

§18.38(iii), §18.38(iii), §18.38(iii).

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13: 19.30 Lengths of Plane Curves

§19.30 Lengths of Plane Curves

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§19.30(i) Ellipse

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§19.30(ii) Hyperbola

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§19.30(iii) Bernoulli’s Lemniscate

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14: Philip J. Davis

… ►This immediately led to discussions among some of the project members about what might be possible, and the discovery that some interactive graphics work had already been done for the NIST Matrix Market, a publicly available repository of test matrices for comparing the effectiveness of numerical linear algebra algorithms. … ►Moreover, a cutting plane feature allows users to track curves of intersection produced as a moving plane cuts through the function surface. …

15: Bibliography S

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Numerics of the generalized Lambert $W$ function. ACM Commun. Comput. Algebra 48 (2), pp. 42–56.

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External Links:

FullText, Document, MathReview Entry, ZentralBlatt

Referenced by:

§4.13, §4.13.

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Asymptotic series of generalized Lambert $W$ function. ACM Commun. Comput. Algebra 47 (3), pp. 75–83.

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External Links:

FullText, ZentralBlatt

Referenced by:

§4.13, §4.13.

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Euler-Maclaurin expansions for integrals with arbitrary algebraic endpoint singularities. Math. Comp. 81 (280), pp. 2159–2173.

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ISSN 0025-5718, Document, Link, MathReview (Vittoria Demichelis), ZentralBlatt

Referenced by:

§2.10(i).

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Euler-Maclaurin expansions for integrals with arbitrary algebraic-logarithmic endpoint singularities. Constr. Approx. 36 (3), pp. 331–352.

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ISSN 0176-4276, Document, Link, MathReview (Razvan A. Mezei), ZentralBlatt

Referenced by:

§2.10(i).

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Rational Points on Elliptic Curves. Undergraduate Texts in Mathematics, Springer-Verlag, New York.

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External Links:

ISBN 0-387-97825-9, MathReview (Andrew Bremner), ZentralBlatt

Referenced by:

§22.18(iv), §23.1, §23.20(ii), §23.20(ii), §23.20(v).

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16: Bibliography M

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Affine Hecke Algebras and Orthogonal Polynomials. Cambridge Tracts in Mathematics, Vol. 157, Cambridge University Press, Cambridge.

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External Links:

ISBN 0-521-82472-9, MathReview (Eric M. Opdam), ZentralBlatt

Referenced by:

§18.37(iii).

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Computational Algebra Group, School of Mathematics and Statistics, University of Sydney, Australia.

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Notes:

A software package (the successor to CAYLEY) designed to solve computationally hard problems in algebra, number theory, geometry, and combinatorics, and to provide a mathematically rigorous environment for computing with algebraic, number-theoretic, combinatoric, and geometric objects.

External Links:

Magma

Referenced by:

4th item.

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Sixth Painlevé Equation, Universal Elliptic Curve, and Mirror of ${𝐏}^2$ . In Geometry of Differential Equations, A. Khovanskii, A. Varchenko, and V. Vassiliev (Eds.), Amer. Math. Soc. Transl. Ser. 2, Vol. 186, pp. 131–151.

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External Links:

MathReview (Bruce Hunt), ZentralBlatt

Referenced by:

§32.2(iv).

Encodings:

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Elliptic Curves. Cambridge University Press, Cambridge.

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Notes:

Reprint with corrections of original edition, published in 1997 by Cambridge University Press

External Links:

ISBN 0-521-58228-8; 0-521-65817-9, MathReview (Amílcar Pacheco), ZentralBlatt

Referenced by:

§20.1, §20.11(i), §20.11(ii), §20.12(i), §20.12(i), §20.12(ii), §20.7(iii), §20.7(v), §20.9(i), §20.9(ii), Ch.20, §22.18(ii), §22.18(iv), Ch.22, §23.1, §23.15(i), §23.20(i), §23.20(ii), §23.20(ii), §23.21(ii), §23.22(ii), §23.6(iv), Ch.23, Notations T.

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Table of the ratio: Area to bounding ordinate, for any portion of normal curve. Biometrika 18, pp. 395–400.

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External Links:

FullText, ZentralBlatt

Referenced by:

§7.8.

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17: Bibliography C

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Work Group of Computational Mathematics, University of Kassel, Germany.

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Notes:

Computer Algebra and Orthogonal Polynomials: a Web service using Maple for online generation of formulas and graphs of orthogonal polynomials belonging to the Askey scheme. For further information see Swarttouw (1997) and Koepf (1999).

External Links:

CAOP

Referenced by:

1st item.

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Algebra: An Elementary Textbook for the Higher Classes of Secondary Schools and for Colleges. 6th edition, Vol. 1, Chelsea Publishing Co., New York.

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Notes:

A seventh edition (reprinting of the sixth edition) was published by AMS Chelsea Publishing Series, American Mathematical Society, 1964.

External Links:

ISBN 978-0-8218-1648-6, Seventh Edition, MathReview, ZentralBlatt

Referenced by:

§1.2(i), §1.2(ii), §1.2(iii), §1.2(iii).

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Algebra: An Elementary Textbook for the Higher Classes of Secondary Schools and for Colleges. 6th edition, Vol. 2, Chelsea Publishing Co., New York.

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Notes:

A seventh edition (reprinting of the sixth edition) was published by AMS Chelsea Publishing Series, American Mathematical Society, 1964.

External Links:

ISBN 978-0-8218-1649-3, Seventh Edition, MathReview, ZentralBlatt

Referenced by:

§1.2(i).

Encodings:

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A Course in Computational Algebraic Number Theory. Springer-Verlag, Berlin-New York.

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External Links:

ISBN 3-540-55640-0, 0-387-55640-0, MathReview (Joe P. Buhler), ZentralBlatt

Referenced by:

§23.17(i), §27.18, §27.18.

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Algorithms for Modular Elliptic Curves. 2nd edition, Cambridge University Press, Cambridge.

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External Links:

ISBN 0-521-59820-6, MathReview (Joseph H. Silverman), ZentralBlatt

Referenced by:

§23.20(ii).

Encodings:

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