Zeilberger–Bressoud theorem

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11: 27 Functions of Number Theory

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12: Bibliography

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Multiple series Rogers-Ramanujan type identities. Pacific J. Math. 114 (2), pp. 267–283.

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External Links:

ISSN 0030-8730, MathReview (David M. Bressoud), ZentralBlatt

Referenced by:

§17.12.

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$q$-Series: Their Development and Application in Analysis, Number Theory, Combinatorics, Physics, and Computer Algebra. CBMS Regional Conference Series in Mathematics, Vol. 66, Amer. Math. Soc., Providence, RI.

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External Links:

ISBN 0-8218-0716-1, MathReview (David M. Bressoud), ZentralBlatt

Referenced by:

§17.14, §17.14, §17.16, Ch.17, Profile George E. Andrews.

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Theorems on generalized Dedekind sums. Pacific J. Math. 2 (1), pp. 1–9.

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External Links:

MathReview (N. G. de Bruijn), ZentralBlatt

Referenced by:

(25.11.41), (25.11.42), §25.11(xii).

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A Centennial History of the Prime Number Theorem. In Number Theory, Trends Math., pp. 1–14.

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External Links:

MathReview (Giovanni Coppola), ZentralBlatt

Referenced by:

(25.16.2), (25.16.4), §25.16(i), §25.16.

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An integral of products of ultraspherical functions and a $q$-extension. J. London Math. Soc. (2) 33 (1), pp. 133–148.

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External Links:

ISSN 0024-6107, MathReview (David M. Bressoud), ZentralBlatt

Referenced by:

§10.22(iv), §14.30(ii).

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13: Bibliography L

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Démonstration d’un Théoréme d’Arithmétique. Nouveau Mém. Acad. Roy. Sci. Berlin, pp. 123–133 (French).

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Notes:

Reprinted in Oeuvres, Vol. 3, pp. 189–201, Gauthier-Villars, Paris, 1867

External Links:

FullText

Referenced by:

§27.13(iii).

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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).

External Links:

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

Referenced by:

§35.12.

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14: 27.19 Methods of Computation: Factorization

… ►Fermat’s algorithm is another; see Bressoud (1989, §5.1). … ►A description of cfrac is given in Bressoud and Wagon (2000). …

15: Bibliography B

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Abelian Functions: Abel’s Theorem and the Allied Theory of Theta Functions. Cambridge University Press, Cambridge.

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Notes:

Reprint of the 1897 original, with a foreword by Igor Krichever.

External Links:

ISBN 0-521-49877-5, MathReview (John B. Little), ZentralBlatt

Referenced by:

§20.9(ii).

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Waves and Thom’s theorem. Advances in Physics 25 (1), pp. 1–26.

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External Links:

Document

Referenced by:

§36.14(i).

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Factorization and Primality Testing. Springer-Verlag, New York.

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External Links:

ISBN 0-387-97040-1, MathReview (Brigitte Vallée), ZentralBlatt

Referenced by:

§23.20(iii), §27.19, Profile David M. Bressoud.

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Proofs and Confirmations: The Story of the Alternating Sign Matrix Conjecture. Cambridge University Press, Cambridge.

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External Links:

ISBN 0-521-66170-6; 0-521-66646-5, MathReview (George E. Andrews), ZentralBlatt

Referenced by:

§1.3(ii), §26.10(ii), §26.10(iii), §26.12(i), §26.12(ii), §26.12(iii), §26.19, §26.20, §26.9(iii), Profile David M. Bressoud.

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A Course in Computational Number Theory. Key College Publishing, Emeryville, CA.

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Notes:

With 1 CD-ROM (Windows, Macintosh and UNIX) containing a collection of Mathematica programs for computations in number theory.

External Links:

ISBN 1-930190-10-7, MathReview (Samuel S. Wagstaff, Jr.), ZentralBlatt

Referenced by:

§27.12, §27.19, §27.21, 2nd item, Profile David M. Bressoud.

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16: 30.10 Series and Integrals

… ►For an addition theorem, see Meixner and Schäfke (1954, p. 300) and King and Van Buren (1973). …

17: 10.44 Sums

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§10.44(i) Multiplication Theorem

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§10.44(ii) Addition Theorems

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Neumann’s Addition Theorem

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Graf’s and Gegenbauer’s Addition Theorems

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18: 26.20 Physical Applications

… ►For an application of statistical mechanics to combinatorics, see Bressoud (1999). …

19: Bibliography W

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An algorithmic proof theory for hypergeometric (ordinary and “$q$”) multisum/integral identities. Invent. Math. 108, pp. 575–633.

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External Links:

ISSN 0020-9910, Document, MathReview (David R. Masson), ZentralBlatt

Referenced by:

§16.4(iii).

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Rational function certification of multisum/integral/“$q$” identities. Bull. Amer. Math. Soc. (N.S.) 27 (1), pp. 148–153.

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External Links:

ISSN 0273-0979, Pdf, Document, MathReview (Robert A. Gustafson), ZentralBlatt

Referenced by:

§16.4(iii).

Encodings:

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20: Software Index

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	Open Source													With Book						Commercial
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26.22 Software						✓						✓									✓	✓	a		Wolfram’s Mathworld, Zeilberger
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35.12 Software																									Zeilberger

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