application to combinatorics

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11: Bibliography L

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Special Functions and Their Applications. Prentice-Hall Inc., Englewood Cliffs, N.J..

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Notes:

R. A. Silverman, translator and editor; reprinted by Dover, New York, 1972.

External Links:

MathReview (A. Erdélyi), ZentralBlatt

Referenced by:

§1.17(iv), Ch.12, §18.18(i), §6.17, §6.7(i), Ch.6, Ch.7, (9.11.3), §9.11(iii), Ch.9.

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An application of the finite element approximation method to find the complex zeros of the modified Bessel function $K_n(z)$ . Math. Comp. 33 (148), pp. 1299–1306.

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ISSN 0025-5718, FullText, MathReview (R. P. Boas, Jr.), ZentralBlatt

Referenced by:

§10.74(vi), 2nd item.

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On incomplete Airy functions and their application to diffraction problems. Radio Sci. 4 (10), pp. 959–969.

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ISSN 0048-6604, Document, MathReview (T. Erber)

Referenced by:

§9.14.

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A systematic “saddle point near a pole” asymptotic method with application to the Gauss hypergeometric function. Stud. Appl. Math. 127 (1), pp. 24–37.

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ISSN 0022-2526, Document, FullText, MathReview (M. S. Mahadeva Naika), ZentralBlatt

Referenced by:

§15.12(ii), §15.12(ii).

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Combinatorics in Pure Mathematics. In Handbook of Combinatorics, Vol. 2, R. L. Graham, M. Grötschel, and L. Lovász (Eds.), pp. 2039–2082.

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External Links:

MathReview, ZentralBlatt

Referenced by:

§26.19.

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12: Bibliography R

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Hypergeometric Functions on Domains of Positivity, Jack Polynomials, and Applications. Contemporary Mathematics, Vol. 138, American Mathematical Society, Providence, RI.

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External Links:

ISBN 0-8218-5159-4, MathReview, ZentralBlatt

Referenced by:

Ch.35, Profile Donald St. P. Richards.

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Research Institute for Symbolic Computation, Hagenberg im Mühlkreis, Austria.

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Notes:

Software packages for hypergeometric and $q$-hypergeometric summation, sequences and power series, permutation groups, partition analysis, and difference equations.

External Links:

RISC Combinatorics Group

Referenced by:

6th item.

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Some Applications of the Lamé Function Solutions of the Linearised Supersonic Flow Equations. Technical Reports and Memoranda Technical Report 2865, Aeronautical Research Council (Great Britain).

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Notes:

Reprinted by Her Majesty’s Stationery Office, London, 1962.

External Links:

MathReview (P. Germain)

Referenced by:

§29.19(ii).

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Elementary Number Theory and its Applications. 5th edition, Addison-Wesley, Reading, MA.

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External Links:

ISBN 0-201-87073-8, MathReview (Norman J. Richert)

Referenced by:

§27.17.

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Combinatorics in Chemistry. In Handbook of Combinatorics, Vol. 2, R. L. Graham, M. Grötschel, and L. Lovász (Eds.), pp. 1955–1981.

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External Links:

MathReview (Haruo Hosoya), ZentralBlatt

Referenced by:

§26.20.

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13: 16.23 Mathematical Applications

§16.23 Mathematical Applications

… ►A variety of problems in classical mechanics and mathematical physics lead to Picard–Fuchs equations. … ►In Janson et al. (1993) limiting distributions are discussed for the sparse connected components of these graphs, and the asymptotics of three ${}_2{}^{}F_2^{}$ functions are applied to compute the expected value of the excess. … ►The Bieberbach conjecture states that if ${\sum }_{n=0}^{\mathrm{\infty }}{a}_n{z}^n$ is a conformal map of the unit disk to any complex domain, then $|a_n|\le n|a_1|$. … ►

§16.23(iv) Combinatorics and Number Theory

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14: Bibliography W

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Extension of a quadratic transformation due to Whipple with an application. Adv. Difference Equ., pp. 2013:157, 8.

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ISSN 1687-1847, Document, FullText, MathReview (Daniele Ritelli), ZentralBlatt

Referenced by:

§16.6, §16.6.

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Asymptotic expansions of some matrix argument hypergeometric functions, with applications to macromolecules. Ann. Inst. Statist. Math. 45 (3), pp. 467–475.

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ISSN 0020-3157, Document, MathReview (N. K. Thakare), ZentralBlatt

Referenced by:

§35.9.

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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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External Links:

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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Notes:

A service of the Electronic Journal of Combinatorics with links to databases, software, and other resources.

External Links:

World Combinatorics Exchange

Referenced by:

8th item.

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15: 18.39 Applications in the Physical Sciences

§18.39 Applications in the Physical Sciences

… ►Shizgal (2015) gives a broad overview of techniques and applications of spectral and pseudo-spectral methods to problems arising in theoretical chemistry, chemical kinetics, transport theory, and astrophysics. … ►

§18.39(v) Other Applications

►For applications of Legendre polynomials in fluid dynamics to study the flow around the outside of a puff of hot gas rising through the air, see Paterson (1983). For applications and an extension of the Szegő–Szász inequality (18.14.20) for Legendre polynomials ($\alpha =\beta =0$) to obtain global bounds on the variation of the phase of an elastic scattering amplitude, see Cornille and Martin (1972, 1974). …

16: 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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Application of the combined nonlinear-condensation transformation to problems in statistical analysis and theoretical physics. Comput. Phys. Comm. 150 (1), pp. 1–20.

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Notes:

Includes algorithms for Lerch’s transcendent. C and Mathematica codes by Aksenov and Jentschura are available.

External Links:

Code, Document

Referenced by:

1st item.

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Applications of basic hypergeometric functions. SIAM Rev. 16 (4), pp. 441–484.

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External Links:

Document, MathReview (L. J. Slater), ZentralBlatt

Referenced by:

§17.16, Ch.17.

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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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Pfaff’s method II: Diverse applications. J. Comput. Appl. Math. 68 (1-2), pp. 15–23.

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External Links:

ISSN 0377-0427, Document, MathReview (Bruce C. Berndt), ZentralBlatt

Referenced by:

§17.7(iii).

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17: Bibliography P

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Introduction to quantum mechanics. Dover Publications, Inc., New York.

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Notes:

With applications to chemistry, Reprint of the 1935 original

External Links:

ISBN 0-486-64871-0, MathReview Entry

Referenced by:

§1.18(v), §18.39(i), §18.39(ii), §18.39(ii).

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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).

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Complex Interval Arithmetic and its Applications. Mathematical Research, Vol. 105, Wiley-VCH Verlag Berlin GmbH, Berlin.

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External Links:

ISBN 3-527-40134-2, MathReview (G. Alefeld), ZentralBlatt

Referenced by:

§3.1(ii).

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Notes on Introductory Combinatorics. Progress in Computer Science, Vol. 4, Birkhäuser Boston Inc., Boston, MA.

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External Links:

ISBN 0-8176-3123-2; 0-8176-3170-4, MathReview (Bernard M. E. Moret), ZentralBlatt

Referenced by:

§26.18.

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Catastrophe Theory and its Applications. Pitman, London.

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Notes:

Reprinted by Dover in 1996.

External Links:

ISBN 0-273-01029-8, MathReview (George K. Francis), ZentralBlatt

Referenced by:

§36.4(i), Ch.36.

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18: Bibliography C

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Combinatorics: Topics, Techniques, Algorithms. Cambridge University Press, Cambridge.

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External Links:

ISBN 0-521-45133-7; 0-521-45761-0, MathReview (E. J. F. Primrose), ZentralBlatt

Referenced by:

§26.13.

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Numerical Grid Methods and Their Application to Schrödinger’s Equation. NATO Advanced Science Institutes Series C: Mathematical and Physical Sciences, Vol. 412, Kluwer Academic Publishers, Dordrecht.

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External Links:

ISBN 0-7923-2423-4, Document, Link, MathReview (M. Znojil)

Referenced by:

§18.38(i).

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Numerical evaluation of the Lambert $W$ function and application to generation of generalized Gaussian noise with exponent 1/2. IEEE Trans. Signal Process. 50 (9), pp. 2160–2165.

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External Links:

ISSN 1053-587X, Document, MathReview (J. Borwein), ZentralBlatt

Referenced by:

§4.44, §4.45(iii).

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On the zeros of the Askey-Wilson polynomials, with applications to coding theory. SIAM J. Math. Anal. 18 (1), pp. 191–207.

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ISSN 0036-1410, Document, MathReview (Mourad E. H. Ismail), ZentralBlatt

Referenced by:

§18.38(iii).

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Schrödinger Operators, with Applications to Quantum Mechanics and Global Geometry. Springer Verlag, New York.

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External Links:

ISBN 978-3-540-16758-7

Referenced by:

§1.18(vii), §1.18(x).

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19: Bibliography S

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Spectral Methods in Chemistry and Physics. Applications to Kinetic Theory and Quantum Mechanics. Scientific Computation, Springer-Verlag, Dordrecht.

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External Links:

ISBN 978-94-017-9453-4; 978-94-017-9454-1, Document, Link, MathReview (Gabriel Stoltz)

Referenced by:

§18.38(i), §18.39(iii), §18.39(iii), §18.39(iii).

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Hypergeometric and Legendre Functions with Applications to Integral Equations of Potential Theory. National Bureau of Standards Applied Mathematics Series, No. 19, U. S. Government Printing Office, Washington, D.C..

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External Links:

MathReview, ZentralBlatt

Referenced by:

§13.23(iv), Ch.14, §31.3(iii).

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Enumerative Combinatorics. Vol. 1. Cambridge University Press, Cambridge.

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Notes:

Corrected reprint of the 1986 original.

External Links:

ISBN 0-521-55309-1; 0-521-66351-2, MathReview (Wayne M. Dymacek), ZentralBlatt

Referenced by:

§26.13, §26.14(i), §26.14(ii), §26.15, §26.17, §26.18, Ch.26.

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Enumerative Combinatorics. Vol. 2. Cambridge University Press, Cambridge.

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External Links:

ISBN 0-521-56069-1, MathReview (Ira Gessel), ZentralBlatt

Referenced by:

§26.18, §26.5(i), §26.6(i), §26.6(ii), §26.6(iv), Ch.26.

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Constructive Combinatorics. Springer-Verlag, New York.

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External Links:

ISBN 0-387-96347-2, MathReview (D. J. Kleitman), ZentralBlatt

Referenced by:

§26.22.

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