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11: 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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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

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4th item.

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New ladder operators for a rational extension of the harmonic oscillator and superintegrability of some two-dimensional systems. J. Math. Phys. 54 (10), pp. Paper 102102, 12 pp..

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MathReview Entry

Referenced by:

§18.36(vi).

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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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SciFace Software, Paderborn, Germany.

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Notes:

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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12: Bibliography R

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Symbolic and extended-precision general purpose computer algebra system.

External Links:

Home Page

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§ ‣ Software Cross Index.

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Methods of Modern Mathematical Physics, Vol. 4, Analysis of Operators. Academic Press, New York.

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ISBN 0-12-585004-2(vol.4), MathReview (P. R. Chernoff)

Referenced by:

§1.18(x).

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On the computation of Lamé functions, of eigenvalues and eigenfunctions of some potential operators. Z. Angew. Math. Mech. 78 (1), pp. 66–72.

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ISSN 0044-2267, Document, MathReview Entry, ZentralBlatt

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§29.20(ii).

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On the foundations of combinatorial theory. VIII. Finite operator calculus. J. Math. Anal. Appl. 42, pp. 684–760.

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ISSN 0022-247X, Document, Link, MathReview (P. Saphar), ZentralBlatt

Referenced by:

§18.2(xii).

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On Simple Waves with Profiles in the form of some Special Functions—Chebyshev-Hermite, Mathieu, Whittaker—in Two-phase Media. In Differential Operators and Related Topics, Vol. I (Odessa, 1997), Operator Theory: Advances and Applications, Vol. 117, pp. 313–322.

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ISBN 3-7643-6287-1, MathReview Entry, ZentralBlatt

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5th item.

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13: 3.1 Arithmetics and Error Measures

… ►The elementary arithmetical operations on intervals are defined as follows: … ►Computer algebra systems use exact rational arithmetic with rational numbers $p/q$, where $p$ and $q$ are multi-length integers. …

14: 21.7 Riemann Surfaces

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§21.7(i) Connection of Riemann Theta Functions to Riemann Surfaces

… ►Belokolos et al. (1994, §2.1)), they are obtainable from plane algebraic curves (Springer (1957), or Riemann (1851)). … ►

§21.7(iii) Frobenius’ Identity

… ►These are Riemann surfaces that may be obtained from algebraic curves of the form …Define the operation …

15: Bibliography L

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Exact operator solution of the Calogero-Sutherland model. Comm. Math. Phys. 178 (2), pp. 425–452.

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Notes:

For a Maple implementation of the algorithm given in this paper for Jack and zonal polynomials see Zeilberger (website).

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ISSN 0010-3616, Link, MathReview (Kazuhiro Hikami), ZentralBlatt

Referenced by:

§35.12.

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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

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§17.16.

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Introduction to spectral theory: selfadjoint ordinary differential operators. Translations of Mathematical Monographs, Vol. 39, American Mathematical Society, Providence, R.I..

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Notes:

Translated from the Russian by Amiel Feinstein

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MathReview Entry

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§1.18(x).

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Evaluation of Bessel function integrals with algebraic singularities. J. Comput. Appl. Math. 37 (1-3), pp. 101–112.

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ISSN 0377-0427, Document, MathReview, ZentralBlatt

Referenced by:

§10.74(vii).

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16: Guide to Searching the DLMF

… ►Search queries are made up of terms, textual phrases, and math expressions, combined with Boolean operators: … ►

and and or

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adj, prec/n, and near/n, where n is any positive natural number.

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$	stands for any number of alphanumeric characters
	(the more conventional * is reserved for the multiplication operator)
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… ►The syntax of the special functions can be LaTeX-like or as employed in widely used computer algebra systems. …

17: Bibliography S

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An Introduction to the Operations with Series. 2nd edition, Chelsea Publishing Co., New York.

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Notes:

This is a reprint, with corrections, of the first edition [University of Pennsylvania Press, Philadelphia, Pa., 1924].

External Links:

MathReview, ZentralBlatt

Referenced by:

§24.1, §24.6.

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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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The Bound State of Weakly Coupled Schrödinger Operators in One and Two Dimensions. Annals of Physics 97 (2), pp. 279–288.

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External Links:

Document, MathReview Entry

Referenced by:

§1.18(viii).

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Operators with Singular Continuous Spectrum: I. General Operators. Annals of Mathematics 141 (1), pp. 131–145.

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MathReview Entry

Referenced by:

§1.18(vii).

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18: 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.

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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

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§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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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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19: Bibliography H

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Solving Ordinary Differential Equations. II. Stiff and Differential-Algebraic Problems. 2nd edition, Springer Series in Computational Mathematics, Vol. 14, Springer-Verlag, Berlin.

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ISBN 3-540-60452-9, MathReview, ZentralBlatt

Referenced by:

§3.7(v).

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Lie groups, Lie algebras, and representations. Second edition, Graduate Texts in Mathematics, Vol. 222, Springer, Cham.

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Notes:

An elementary introduction

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ISBN 978-3-319-13466-6; 978-3-319-13467-3, Document, Link, MathReview Entry

Referenced by:

§1.2(vi).

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Asymptotic expansion of a class of integral transforms with algebraically dominated kernels. J. Math. Anal. Appl. 35 (2), pp. 405–433.

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Document, MathReview (E. L. Koh), ZentralBlatt

Referenced by:

§2.5(ii).

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An elementary approach to the hypergeometric shift operators of Opdam. Invent. Math. 103 (2), pp. 341–350.

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ISSN 0020-9910, Document, MathReview (Eric M. Opdam), ZentralBlatt

Referenced by:

§18.37(iii).

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Vector Calculus, Linear Algebra, and Differential Forms: A Unified Approach. 2nd edition, Prentice Hall Inc., Upper Saddle River, NJ.

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External Links:

ISBN 0-13-041408-5; 978-0-13-041408-3, MathReview (W. P. Ziemer), ZentralBlatt

Referenced by:

§1.6(i).

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20: Philip J. Davis

… ►At that time John Todd was Chief of the Numerical Analysis Section of the Applied Mathematics Division and head of the Computation Laboratory that co-developed, with the NBS Electronic Computer Laboratory, the Standards Eastern Automatic Computer (SEAC), the first fully operational stored-program electronic digital computer in the United States. … ►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. …