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1: 27.22 Software

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Maple. isprime combines a strong pseudoprime test and a Lucas pseudoprime test. ifactor uses cfrac (§27.19) after exhausting trial division. Brent–Pollard rho, Square Forms Factorization, and ecm are available also; see §27.19.

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Mathematica. PrimeQ combines strong pseudoprime tests for the bases 2 and 3 and a Lucas pseudoprime test. No known composite numbers pass these three tests, and Bleichenbacher (1996) has shown that this combination of tests proves primality for integers below ${10}^{16}$. Provable PrimeQ uses the Atkin–Goldwasser–Kilian–Morain Elliptic Curve Method to prove primality. FactorInteger tries Brent–Pollard rho, Pollard $p-1$, and then cfrac after trial division. See §27.19. ecm is available also, and the Multiple Polynomial Quadratic sieve is expected in a future release.

For additional Mathematica routines for factorization and primality testing, including several different pseudoprime tests, see Bressoud and Wagon (2000).

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2: Charles W. Clark

… ► Taylor), published by Plenum Press in 1988, and Atoms in Strong Fields (with M. …

3: 17.12 Bailey Pairs

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Strong Bailey Lemma

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4: Philip J. Davis

… ►In 1957, Davis took over as Chief, Numerical Analysis Section when John Todd and his wife Olga Taussky-Todd, feeling a strong pull toward teaching and research, left to pursue full-time positions at the California Institute of Technology. …

5: Bibliography I

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Statistical Field Theory: Strong Coupling, Monte Carlo Methods, Conformal Field Theory, and Random Systems. Vol. 2, Cambridge University Press, Cambridge.

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External Links:

ISBN 0-521-37012-4; 0-521-40806-7, MathReview (C. A. Hurst), ZentralBlatt

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2nd item.

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6: Bibliography D

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Strong and ratio asymptotics for Laguerre polynomials revisited. J. Math. Anal. Appl. 403 (2), pp. 477–486.

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External Links:

ISSN 0022-247X, Document, FullText, MathReview (Pablo Manuel Román), ZentralBlatt

Referenced by:

§18.15(iv), §18.15(iv).

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BibTeX

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Strong asymptotics of orthogonal polynomials with respect to exponential weights. Comm. Pure Appl. Math. 52 (12), pp. 1491–1552.

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External Links:

ISSN 0010-3640, Document, MathReview (D. S. Lubinsky), ZentralBlatt

Referenced by:

§18.32.

Encodings:

BibTeX

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7: Bibliography G

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Quantum Electrodynamics of Strong Fields: With an Introduction into Modern Relativistic Quantum Mechanics. Texts and Monographs in Physics, Springer.

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Referenced by:

§33.22(iv).

Encodings:

BibTeX

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8: Bibliography K

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Strong asymptotics of polynomials orthogonal with respect to Freud weights. Internat. Math. Res. Notices 1999 (6), pp. 299–333.

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External Links:

ISSN 1073-7928, Document, MathReview (Heinrich Begehr), ZentralBlatt

Referenced by:

§18.32.

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BibTeX

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