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11: 23.21 Physical Applications

§23.21 Physical Applications

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12: Bibliography S

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The Gaussian Function in Calculations of Statistical Mechanics and Quantum Mechanics. In Methods in Computational Physics: Advances in Research and Applications, B. Alder, S. Fernbach, and M. Rotenberg (Eds.), Vol. 2, pp. 1–45.

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Referenced by:

§8.24(i), §8.24(iii).

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13: Bibliography P

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Statistical Field Theory. Addison-Wesley, Reading, MA.

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External Links:

ISBN 0-201-05985-1, MathReview (Tony C. Dorlas), ZentralBlatt

Referenced by:

§22.19(ii).

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Zonal Polynomials of Order $1$ Through $12$ . In Selected Tables in Mathematical Statistics, H. L. Harter and D. B. Owen (Eds.), Vol. 2, pp. 199–388.

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External Links:

MathReview

Referenced by:

§35.11.

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The exact distribution of the Wald statistic. Econometrica 54 (4), pp. 881–895.

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External Links:

ISSN 0012-9682, FullText, MathReview (Sadanori Konishi), ZentralBlatt

Referenced by:

§35.9.

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Stacking models of vesicles and compact clusters. J. Statist. Phys. 80 (3–4), pp. 755–779.

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External Links:

Document, ZentralBlatt

Referenced by:

§8.24(ii).

Encodings:

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Elliptic integrals. Computers in Physics 4 (1), pp. 92–96.

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Referenced by:

2nd item.

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14: Hans Volkmer

… ►He studied mathematics and physics at the University of Konstanz. … ►Volkmer has published numerous papers on special functions, spectral theory, differential equations, and mathematical statistics. …

15: 8.24 Physical Applications

§8.24 Physical Applications

… ►The function $\gamma (a,x)$ appears in: discussions of power-law relaxation times in complex physical systems (Sornette (1998)); logarithmic oscillations in relaxation times for proteins (Metzler et al. (1999)); Gaussian orbitals and exponential (Slater) orbitals in quantum chemistry (Shavitt (1963), Shavitt and Karplus (1965)); population biology and ecological systems (Camacho et al. (2002)). ►

§8.24(ii) Incomplete Beta Functions

►The function $I_x(a,b)$ appears in: Monte Carlo sampling in statistical mechanics (Kofke (2004)); analysis of packings of soft or granular objects (Prellberg and Owczarek (1995)); growth formulas in cosmology (Hamilton (2001)). …

16: 5.20 Physical Applications

§5.20 Physical Applications

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Solvable Models of Statistical Mechanics

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17: Bibliography I

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An integral which occurs in statistics. Proceedings of the Cambridge Philosophical Society 29, pp. 271–276.

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External Links:

Document, ZentralBlatt

Referenced by:

§35.3(i), §35.3(ii).

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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

Referenced by:

2nd item.

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Quantum Field Theory. International Series in Pure and Applied Physics, McGraw-Hill International Book Co., New York.

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Notes:

Reprinted by Dover, 2006.

External Links:

ISBN 0-07-032071-3, MathReview (V. E. Korepin)

Referenced by:

§22.19(ii).

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18: Peter A. Clarkson

… … ►is Professor of Mathematics in the School of Mathematics, Statistics, and Actuarial Science at the University of Kent, Canterbury, U. … ►He is also coauthor of the book From Nonlinearity to Coherence: Universal Features of Nonlinear Behaviour in Many-Body Physics (with J. … ►Institute of Physics in 1999, and of the U. …

19: 31.17 Physical Applications

§31.17 Physical Applications

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§31.17(ii) Other Applications

►Heun functions appear in the theory of black holes (Kerr (1963), Teukolsky (1972), Chandrasekhar (1984), Suzuki et al. (1998), Kalnins et al. (2000)), lattice systems in statistical mechanics (Joyce (1973, 1994)), dislocation theory (Lay and Slavyanov (1999)), and solution of the Schrödinger equation of quantum mechanics (Bay et al. (1997), Tolstikhin and Matsuzawa (2001), and Hall et al. (2010)). … ►More applications—including those of generalized spheroidal wave functions and confluent Heun functions in mathematical physics, astrophysics, and the two-center problem in molecular quantum mechanics—can be found in Leaver (1986) and Slavyanov and Lay (2000, Chapter 4). …

20: Bibliography C

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Statistics on Special Manifolds. Lecture Notes in Statistics, Vol. 174, Springer-Verlag, New York.

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External Links:

ISBN 0-387-00160-3, MathReview (M. Hušková), ZentralBlatt

Referenced by:

§35.9.

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Coulomb phase shift. American Journal of Physics 47 (8), pp. 683–684.

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External Links:

Document

Referenced by:

§5.20.

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Some non-central distribution problems in multivariate analysis. Ann. Math. Statist. 34 (4), pp. 1270–1285.

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External Links:

FullText, MathReview (I. Olkin), ZentralBlatt

Referenced by:

§35.4(i), §35.4(ii).

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Methods of mathematical physics. Vol. I. Interscience Publishers, Inc., New York, N.Y..

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External Links:

MathReview (J. B. Diaz), ZentralBlatt

Referenced by:

(14.30.8_5).

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Algorithm AS 24: From normal integral to deviate. Appl. Statist. 18 (3), pp. 290–293.

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Notes:

Includes Fortran program, maximum accuracy 12D.

External Links:

FullText

Referenced by:

§7.25(ii).

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