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1: Bibliography G

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The GAP Group, Centre for Interdisciplinary Research in Computational Algebra, University of St. Andrews, United Kingdom.

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Groups, Algorithms, Programming: A system for computational discrete algebra with emphasis on computational group theory.

External Links:

GAP

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2nd item.

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Applications of the classical umbral calculus. Algebra Universalis 49 (4), pp. 397–434.

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ISSN 0002-5240, Document, MathReview (George E. Andrews), ZentralBlatt

Referenced by:

§24.4(viii).

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Riemann surfaces, plane algebraic curves and their period matrices. J. Symbolic Comput. 26 (6), pp. 789–803.

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ISSN 0747-7171, Document, MathReview (Gabino González Díez), ZentralBlatt

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1st item.

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Algorithm 939: computation of the Marcum Q-function. ACM Trans. Math. Softw. 40 (3), pp. 20:1–20:21.

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Includes Fortran program claiming 12S accuracy

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

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3rd item, §10.77(ix).

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Mutual integrability, quadratic algebras, and dynamical symmetry. Ann. Phys. 217 (1), pp. 1–20.

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ISSN 0003-4916, Link, MathReview (A. O. Barut), ZentralBlatt

Referenced by:

§18.38(iii).

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2: Bibliography K

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Gravitational field of a spinning mass as an example of algebraically special metrics. Phys. Rev. Lett. 11 (5), pp. 237–238.

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Document, MathReview (C. Gilbert), ZentralBlatt

Referenced by:

§31.17(ii).

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Algebraic Aspects of Cryptography. Springer-Verlag, Berlin.

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Notes:

Second printing with corrections

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

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§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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FullText, MathReview Entry, ZentralBlatt

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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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ISSN 0022-2488, Document, MathReview, ZentralBlatt

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

Referenced by:

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

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3: Bibliography C

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

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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

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1st item.

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

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

Referenced by:

§26.8(vii).

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

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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.

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

Referenced by:

§1.2(i).

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

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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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4: Bibliography D

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Recherches analytiques sur la théorie des nombres premiers. Deuxième partie. Les fonctions de Dirichlet et les nombres premiers de la forme linéaire $Mx+N$ . Ann. Soc. Sci. Bruxelles 20, pp. 281–397 (French).

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Reprinted in Collected works/Oeuvres scientifiques, Vol. I, pp. 309–425, Académie Royale de Belgique, Brussels, 2000.

External Links:

MathReview, ZentralBlatt

Referenced by:

§25.10(i), §27.11, §27.2(i).

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Computing Riemann matrices of algebraic curves. Phys. D 152/153, pp. 28–46.

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ISSN 0167-2789, Document, MathReview (John B. Little), ZentralBlatt

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3rd item.

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Complex zeros of cylinder functions. Math. Comp. 20 (94), pp. 215–222.

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For a numerical error in one of the zeros see Amos (1985).

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ISSN 0025-5718, FullText, MathReview, ZentralBlatt

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2nd item.

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Abstract Algebra. 2nd edition, Prentice Hall Inc., Englewood Cliffs, N.J..

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ISBN 0-13-569302-0, MathReview (N. Popescu), ZentralBlatt

Referenced by:

§1.11(i), §1.11(ii), §1.11(iii).

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Uniform asymptotic expansions for Whittaker’s confluent hypergeometric functions. SIAM J. Math. Anal. 20 (3), pp. 744–760.

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Notes:

(This reference has several typographical errors.)

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ISSN 0036-1410, Document, MathReview (F. W. J. Olver), ZentralBlatt

Referenced by:

§13.21(ii), §13.21(iii), §13.21(iv).

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5: 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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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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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

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4th item.

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On a class of algebraic solutions to the Painlevé VI equation, its determinant formula and coalescence cascade. Funkcial. Ekvac. 46 (1), pp. 121–171.

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ISSN 0532-8721, FullText, MathReview (Andrew Pickering), ZentralBlatt

Referenced by:

§32.9(iii).

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

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

Referenced by:

§18.27(v).

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SciFace Software, Paderborn, Germany.

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Computer algebra system for doing symbolic and exact algebraic computations as well as numerical calculations with almost arbitrary accuracy

Referenced by:

§ ‣ Software Cross Index.

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