De%20Moivre%20theorem

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11: 4.21 Identities

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De Moivre’s Theorem

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12: Bibliography L

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Essai sur la Théorie des Nombres. 2nd edition, Courcier, Paris.

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External Links:

ZentralBlatt

Referenced by:

§27.2(i).

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Traité des fonctions elliptiques et des intégrales Eulériennes. Huzard-Courcier, Paris.

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Notes:

vol.1, 1825; vol.2, 1826; three supplements, 1828–1832.

Referenced by:

§19.14(ii), Ch.19.

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Le Calcul des Résidus et ses Applications à la Théorie des Fonctions. Gauthier-Villars, Paris (French).

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Notes:

Reprinted by Éditions Jacques Gabay, Sceaux, 1989.

External Links:

ISBN 2-87647-060-8, MathReview, ZentralBlatt

Referenced by:

(25.5.10), (25.5.11), (25.5.12).

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Sur la distribution des nombres premiers. Comptes Rendus de l’Academie des Sciences, Paris 158, pp. 1869–1872 (French).

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External Links:

ZentralBlatt

Referenced by:

§27.12.

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Théorie des nombres. Tome I: Le calcul des nombres entiers, le calcul des nombres rationnels, la divisibilité arithmétique. Gauthier-Villars, Paris (French).

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External Links:

MathReview (W. J. LeVeque), ZentralBlatt

Referenced by:

§24.1, §24.1.

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13: Bibliography K

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The Riemann Zeta-Function. de Gruyter Expositions in Mathematics, Vol. 5, Walter de Gruyter & Co., Berlin.

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Notes:

Translated from the Russian by Neal Koblitz

External Links:

ISBN 3-11-013170-6, MathReview (Matti Jutila), ZentralBlatt

Referenced by:

Ch.25.

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Algorithm 737: INTLIB: A portable Fortran 77 interval standard-function library. ACM Trans. Math. Software 20 (4), pp. 447–459.

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External Links:

ISSN 0098-3500, Document, GAMS (module 737; package TOMS), ZentralBlatt

Referenced by:

1st item.

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Sur le problème de la rotation d’un corps solide autour d’un point fixe. Acta Math. 12 (1), pp. 177–232 (French).

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External Links:

ISSN 0001-5962, Document, MathReview Entry, ZentralBlatt

Referenced by:

§22.19(iv).

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HYP and HYPQ. Mathematica packages for the manipulation of binomial sums and hypergeometric series respectively $q$-binomial sums and basic hypergeometric series. Séminaire Lotharingien de Combinatoire 30, pp. 61–76.

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Notes:

Also published in J. Symbolic Comput. (1995), v. 20, no. 5–6, pp. 737–744.

External Links:

Code, Document, MathReview (G. Gasper), ZentralBlatt

Referenced by:

1st item.

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The Korteweg-de Vries Equation and Related Evolution Equations. In Nonlinear Wave Motion (Proc. AMS-SIAM Summer Sem., Clarkson Coll. Tech., Potsdam, N.Y., 1972), A. C. Newell (Ed.), Lectures in Appl. Math., Vol. 15, pp. 61–83.

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External Links:

MathReview (G. L. Lamb, Jr.), ZentralBlatt

Referenced by:

§22.19(iii).

Encodings:

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14: Bibliography P

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La Théorie des Fonctions de Bessel Exposée en vue de ses Applications à la Physique Mathématique. Centre National de la Recherche Scientifique, Paris (French).

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External Links:

MathReview (A. Erdélyi), ZentralBlatt

Referenced by:

§10.63(ii).

Encodings:

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Automatic computation of Bessel function integrals. Comput. Phys. Comm. 25 (3), pp. 289–295.

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Notes:

Double-precision Fortran, maximum accuracy 20S.

External Links:

ISSN 0010-4655, Document, Code

Referenced by:

6th item.

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Sur une généralisation des polynomes de Legendre. C. R. Acad. Sci. Paris 228, pp. 1363–1365.

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External Links:

ISSN 0001-4036, MathReview (G. Szegö)

Referenced by:

§18.35(i).

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Systèmes de polynomes biorthogonaux qui généralisent les polynomes ultrasphériques. C. R. Acad. Sci. Paris 228, pp. 1998–2000.

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External Links:

ISSN 0001-4036, MathReview (G. Szegö)

Referenced by:

§18.35(i).

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Sur une famille de polynômes orthogonaux à quatre paramètres. C. R. Acad. Sci. Paris 230, pp. 2254–2256.

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External Links:

MathReview (A. Erdélyi)

Referenced by:

(18.30.17), (18.30.18), (18.35.6_5), (18.35.6_6), §18.35(i).

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15: Bibliography

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Exact linearization of a Painlevé transcendent. Phys. Rev. Lett. 38 (20), pp. 1103–1106.

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External Links:

Document, MathReview (Mark Adler)

Referenced by:

§32.11(ii), §32.13(i), §32.13(ii), §32.13(iii), §32.5.

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On the degrees of irreducible factors of higher order Bernoulli polynomials. Acta Arith. 62 (4), pp. 329–342.

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External Links:

ISSN 0065-1036, Pdf, MathReview (L. Skula), ZentralBlatt

Referenced by:

§24.12(iii).

Encodings:

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Rational and elliptic solutions of the Korteweg-de Vries equation and a related many-body problem. Comm. Pure Appl. Math. 30 (1), pp. 95–148.

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External Links:

MathReview (Alexander A. Pankov), ZentralBlatt

Referenced by:

§23.21(ii).

Encodings:

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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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Fonctions hypergéométriques et hypersphériques. Polynomes d’Hermite. Gauthier-Villars, Paris.

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External Links:

ZentralBlatt

Referenced by:

§16.13, §16.15, Ch.16.

Encodings:

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16: Bibliography V

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Light Scattering by Small Particles. John Wiley and Sons. Inc., New York.

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External Links:

MathReview (P. M. Morse)

Referenced by:

§9.16.

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Multiple Light Scattering. Vol. 1, Academic Press, New York.

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Referenced by:

§6.17.

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On the zeros of the Riemann zeta function in the critical strip. IV. Math. Comp. 46 (174), pp. 667–681.

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External Links:

ISSN 0025-5718, FullText, Document, MathReview (Jürgen G. Hinz), ZentralBlatt

Referenced by:

§25.10(ii), §25.18(ii).

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On the series expansion method for computing incomplete elliptic integrals of the first and second kinds. Math. Comp. 23 (105), pp. 61–69.

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External Links:

FullText, MathReview, ZentralBlatt

Referenced by:

§19.12, §19.5.

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Error estimates for Rayleigh-Ritz approximations of eigenvalues and eigenfunctions of the Mathieu and spheroidal wave equation. Constr. Approx. 20 (1), pp. 39–54.

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External Links:

ISSN 0176-4276, Document, MathReview, ZentralBlatt

Referenced by:

§30.16(i), §30.16(ii), §30.16(ii).

Encodings:

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17: Bibliography B

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Pionic atoms. Annual Review of Nuclear and Particle Science 20, pp. 467–508.

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External Links:

Document

Referenced by:

§33.22(iv).

Encodings:

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Coulomb functions (negative energies). Comput. Phys. Comm. 20 (3), pp. 447–458.

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Notes:

Double-precision Fortran code.

External Links:

Document, Code

Referenced by:

1st item, 4th item.

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Nouvelles Tables d’Intégrales Définies. P. Engels, Leide.

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Notes:

Corrected edition printed by Hafner Press, 1965.

Referenced by:

§1.4(iv).

Encodings:

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Nouvelles Tables d’Intégrales Définies. G.E. Stechert & Co., New York.

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Referenced by:

§4.10(iii), §4.26(v), §4.40(v), §6.14(iii), §6.7(iv).

Encodings:

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Recherches sur les transcendantes de M. Painlevé et l’étude asymptotique des équations différentielles du second ordre. Ann. Sci. École Norm. Sup. (3) 30, pp. 255–375.

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External Links:

ISSN 0012-9593, MathReview Entry, ZentralBlatt

Referenced by:

§32.12(i), §32.12(ii).

Encodings:

BibTeX

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18: Peter L. Walker

… ►Walker’s books are An Introduction to Complex Analysis, published by Hilger in 1974, The Theory of Fourier Series and Integrals, published by Wiley in 1986, Elliptic Functions. A Constructive Approach, published by Wiley in 1996, and Examples and Theorems in Analysis, published by Springer in 2004. … ►

20 Theta Functions

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19: 8 Incomplete Gamma and Related
Functions

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20: 28 Mathieu Functions and Hill’s Equation

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