Borel transform theory

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11: 26.19 Mathematical Applications

§26.19 Mathematical Applications

… ►Partitions and plane partitions have applications to representation theory (Bressoud (1999), Macdonald (1995), and Sagan (2001)) and to special functions (Andrews et al. (1999) and Gasper and Rahman (2004)). ►Other areas of combinatorial analysis include graph theory, coding theory, and combinatorial designs. These have applications in operations research, probability theory, and statistics. …

12: Bruce R. Miller

… ►While developing the supporting theories, he discovered a passion for symbolic computation and computer algebra. …There, he carried out research in non-linear dynamics and celestial mechanics, developing a specialized computer algebra system for high-order Lie transformations. …

13: Bibliography W

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Analytic Theory of Continued Fractions. D. Van Nostrand Company, Inc., New York.

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Notes:

Reprinted by Chelsea Publishing, New York, 1973 and AMS Chelsea Publishing, Providence, RI, 2000.

External Links:

ISBN 0-8218-2106-7, MathReview (R. C. Buck), ZentralBlatt

Referenced by:

§3.10(iii), §4.25, §4.9(i), §4.9(ii), Ch.4, §5.10.

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Linear Turning Point Theory. Applied Mathematical Sciences No. 54, Springer-Verlag, New York.

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ISBN 0-387-96046-5, MathReview (Anthony Leung), ZentralBlatt

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Ch.9.

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A presentation of cnoidal wave theory for practical application. J. Fluid Mech. 7 (2), pp. 273–286.

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Document, MathReview (T. B. Benjamin), ZentralBlatt

Referenced by:

§21.9.

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Group Theory and its Application to the Quantum Mechanics of Atomic Spectra. Pure and Applied Physics. Vol. 5, Academic Press, New York.

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Notes:

Expanded and improved ed. Translated from the German by J. J. Griffin.

External Links:

ISBN 0-12-750550-4, MathReview (A. S. Wightman), ZentralBlatt

Referenced by:

§34.12.

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Elliptic genera and quantum field theory. Comm. Math. Phys. 109 (4), pp. 525–536.

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ISSN 0010-3616, Document, MathReview (J. Stasheff), ZentralBlatt

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1st item.

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14: Bibliography N

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The Development of Prime Number Theory: From Euclid to Hardy and Littlewood. Springer-Verlag, Berlin.

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External Links:

ISBN 3-540-66289-8, MathReview (D. R. Heath-Brown), ZentralBlatt

Referenced by:

§27.12.

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Scattering theory of waves and particles. Dover Publications, Inc., Mineola, NY.

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Notes:

Reprint of the 1982 second edition [Springer, New York; MR0666397 (84f:81001)], with list of errata prepared for this edition by the author

External Links:

ISBN 0-486-42535-5, MathReview Entry

Referenced by:

§1.18(vi), §1.18(viii).

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Handbuch der Theorie der Gammafunktion. B. G. Teubner, Leipzig (German).

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Notes:

For a reprint with corrections see Nielsen (1965).

External Links:

ZentralBlatt (G. Kowalewski)

Referenced by:

§5.12, Ch.5, §6.10(i), §6.10(i), §7.9, §8.1.

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Die Gammafunktion. Band I. Handbuch der Theorie der Gammafunktion. Band II. Theorie des Integrallogarithmus und verwandter Transzendenten. Chelsea Publishing Co., New York (German).

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Notes:

Both books are textually unaltered except for correction of errata.

External Links:

MathReview

Referenced by:

N. Nielsen (1906a), N. Nielsen (1906b).

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Notes:

References and links to software for factorization and primality testing.

External Links:

Home Page

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6th item.

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15: 18.38 Mathematical Applications

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Approximation Theory

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Complex Function Theory

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Random Matrix Theory

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Radon Transform

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Coding Theory

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16: Bibliography U

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On the transformation group of the second Painlevé equation. Nagoya Math. J. 157, pp. 15–46.

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ISSN 0027-7630, MathReview (Andrei A. Kapaev), ZentralBlatt

Referenced by:

§32.7(viii).

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Theory of the Whittaker-Hill equation. Proc. Roy. Soc. Edinburgh Sect. A 69, pp. 28–44.

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External Links:

MathReview (R. K. Rathy), ZentralBlatt

Referenced by:

§28.31(i), §28.31(ii), §28.32(ii).

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Elementary Number Theory. McGraw-Hill Book Company, Inc., New York.

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External Links:

MathReview (D. H. Lehmer), ZentralBlatt

Referenced by:

§24.10(iii).

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17: Bibliography

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Theory of Incomplete Cylindrical Functions and Their Applications. Springer-Verlag, Berlin.

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Notes:

Translated from the Russian by H. E. Fettis, J. W. Goresh and D. A. Lee, Die Grundlehren der mathematischen Wissenschaften, Band 160

External Links:

MathReview, ZentralBlatt

Referenced by:

1st item.

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Complex Analysis: An Introduction of the Theory of Analytic Functions of One Complex Variable. 2nd edition, McGraw-Hill Book Co., New York.

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Notes:

A third edition was published in 1978 by McGraw-Hill, New York.

External Links:

MathReview (P. Lelong), ZentralBlatt

Referenced by:

§1.9(iii), §23.18.

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Unsteady lifting-line theory as a singular-perturbation problem. J. Fluid Mech 153, pp. 59–81.

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External Links:

Document, ZentralBlatt

Referenced by:

§11.12.

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Shanks’ convergence acceleration transform, Padé approximants and partitions. J. Combin. Theory Ser. A 43 (1), pp. 70–84.

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ISSN 0097-3165, Document, MathReview (Kenneth A. Jukes), ZentralBlatt

Referenced by:

§17.18.

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Number Theory. In The New Encyclopaedia Britannica, Vol. 25, pp. 14–37.

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Referenced by:

§27.13(i), §27.15, §27.16, Ch.27.

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18: Bibliography S

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The Laplace Transform: Theory and Applications. Undergraduate Texts in Mathematics, Springer-Verlag, New York.

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External Links:

ISBN 0-387-98698-7, MathReview (Philip Heywood), ZentralBlatt

Referenced by:

§1.14(iii), §1.14(vii).

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Quantum defect theory. Rep. Prog. Phys. 46 (2), pp. 167–257.

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External Links:

Document

Referenced by:

§33.14(i), §33.22(ii).

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Practical Extrapolation Methods: Theory and Applications. Cambridge Monographs on Applied and Computational Mathematics, Vol. 10, Cambridge University Press, Cambridge.

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External Links:

ISBN 0-521-66159-5, MathReview (Thomas A. Atchison), ZentralBlatt

Referenced by:

§3.9(vi).

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Über die analytische Theorie der quadratischen Formen. Ann. of Math. (2) 36 (3), pp. 527–606.

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ISSN 0003-486X, FullText, MathReview Entry, ZentralBlatt

Referenced by:

§35.2.

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A Guide to Distribution Theory and Fourier Transforms. Studies in Advanced Mathematics, CRC Press, Boca Raton, FL.

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ISBN 0-8493-8273-4, MathReview (J. Horváth), ZentralBlatt

Referenced by:

§18.17(v).

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19: Bibliography T

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The Theory of Functions. 2nd edition, Oxford University Press, Oxford.

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External Links:

ZentralBlatt

Referenced by:

§1.10(ix), §1.10(v), §1.8(i), §1.8(ii), §1.8(iii), §1.9(vii).

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On the theory of the Bernoulli polynomials and numbers. J. Math. Anal. Appl. 104 (2), pp. 309–350.

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ISSN 0022-247X, Document, MathReview (Louis Shapiro), ZentralBlatt

Referenced by:

§24.15(iii).

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Combinatorial Group Theory, Riemann Surfaces and Differential Equations. In Contributions to Group Theory, Contemp. Math., Vol. 33, pp. 467–519.

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External Links:

MathReview (William Harvey), ZentralBlatt

Referenced by:

2nd item.

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On a function which occurs in the theory of the structure of polymers. Ann. of Math. (2) 46, pp. 144–157.

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External Links:

FullText, MathReview (I. Niven), ZentralBlatt

Referenced by:

§25.12(ii), Notations P.

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An Essay Toward a Unified Theory of Special Functions. Annals of Mathematics Studies, no. 18, Princeton University Press, Princeton, N.J..

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External Links:

MathReview (A. Erdélyi), ZentralBlatt

Referenced by:

§18.5(ii).

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20: 27.14 Unrestricted Partitions

… ►Euler’s pentagonal number theorem states that … ►Dedekind sums occur in the transformation theory of the Dedekind modular function $\eta \left(\tau \right)$, defined by … ►For example, the Ramanujan identity … ►

§27.14(vi) Ramanujan’s Tau Function

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