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21: Guide to Searching the DLMF

… ►To recognize the math symbols and structures, and to accommodate equivalence between various notations and various forms of expression, the search system maps the math part of your queries into a different form. … ►The syntax of the special functions can be LaTeX-like or as employed in widely used computer algebra systems. …Note that the first form may match other functions $K$ than the Bessel $K$ function, so if you are sure you want Bessel $K$, you might as well enter one of the other 3 forms. …

22: 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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Intégrandes à deux formes quadratiques. C. R. Acad. Sci. Paris Sér. A–B 274 (15 May, 1972, Sér. A), pp. 1458–1461 (French).

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External Links:

MathReview (J. A. Donaldson), ZentralBlatt

Referenced by:

§19.31.

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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).

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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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23: 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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External Links:

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

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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24: 32.9 Other Elementary Solutions

… ►Then ${\text{P}}_{\text{III}}$ has algebraic solutions iff … ► ${\text{P}}_{\text{V}}$, with $\delta =0$, has algebraic solutions if either … ►An elementary algebraic solution of ${\text{P}}_{\text{VI}}$ is … ►Dubrovin and Mazzocco (2000) classifies all algebraic solutions for the special case of ${\text{P}}_{\text{VI}}$ with $\beta =\gamma =0$, $\delta =\frac{1}{2}$. For further examples of algebraic solutions see Andreev and Kitaev (2002), Boalch (2005, 2006), Gromak et al. (2002, §48), Hitchin (2003), Masuda (2003), and Mazzocco (2001b). …

25: 34.2 Definition: $\mathit{3}j$ Symbol

… ►They must form the sides of a triangle (possibly degenerate). … ►where ${}_3{}^{}F_2^{}$ is defined as in §16.2. …

26: 3.2 Linear Algebra

§3.2 Linear Algebra

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§3.2(iii) Condition of Linear Systems

… ► ►The $p$-norm of a matrix $𝐀=[a_{jk}]$ is … ►Then we have the a posteriori error bound …

27: 2.1 Definitions and Elementary Properties

… ►means that for each $n$, the difference between $f(x)$ and the $n$th partial sum on the right-hand side is $O\left({(x-c)}^n\right)$ as $x\to c$ in $𝐗$. … ►Asymptotic expansions of the forms (2.1.14), (2.1.16) are unique. …

28: 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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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).

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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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External Links:

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

Referenced by:

§2.10(i).

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29: 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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Notes:

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

External Links:

GAP

Referenced by:

2nd item.

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

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External Links:

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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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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Special functions of matrix argument. I. Algebraic induction, zonal polynomials, and hypergeometric functions. Trans. Amer. Math. Soc. 301 (2), pp. 781–811.

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External Links:

ISSN 0002-9947, FullText, MathReview (Wayne J. Holman, III), ZentralBlatt

Referenced by:

§35.8(i), §35.8(ii), §35.8(iv), Ch.35.

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30: 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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Notes:

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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Formes canoniques des équations confluentes de l’équation de Heun. Ann. Soc. Sci. Bruxelles Sér. I 92 (1-2), pp. 53–78.

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External Links:

MathReview (A. E. Danese), ZentralBlatt

Referenced by:

§31.12.

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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

Referenced by:

3rd item.

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

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External Links:

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

Referenced by:

§1.11(i), §1.11(ii), §1.11(iii).

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