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1: 26.19 Mathematical Applications
§26.19 Mathematical Applications
Combinatorics has applications to analysis, algebra, and geometry. …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)). … These have applications in operations research, probability theory, and statistics. …
2: 6.17 Physical Applications
§6.17 Physical Applications
Geller and Ng (1969) cites work with applications from diffusion theory, transport problems, the study of the radiative equilibrium of stellar atmospheres, and the evaluation of exchange integrals occurring in quantum mechanics. For applications in astrophysics, see also van de Hulst (1980). Lebedev (1965) gives an application to electromagnetic theory (radiation of a linear half-wave oscillator), in which sine and cosine integrals are used.
3: 26.20 Physical Applications
§26.20 Physical Applications
An English translation of Pólya (1937) on applications of combinatorics to chemistry has been published as Pólya and Read (1987). …The latter reference also describes chemical applications of other combinatorial techniques. … For an application of statistical mechanics to combinatorics, see Bressoud (1999). Other applications to problems in engineering, crystallography, biology, and computer science can be found in Beckenbach (1981) and Graham et al. (1995).
4: 32.16 Physical Applications
§32.16 Physical Applications
Statistical Physics
Integrable Continuous Dynamical Systems
Other Applications
For applications in string theory see Seiberg and Shih (2005).
5: 17.16 Mathematical Applications
§17.16 Mathematical Applications
These and other applications are described in the surveys Andrews (1974, 1986). More recent applications are given in Gasper and Rahman (2004, Chapter 8) and Fine (1988, Chapters 1 and 2).
6: 9.15 Mathematical Applications
§9.15 Mathematical Applications
7: 24.18 Physical Applications
§24.18 Physical Applications
8: 4.44 Other Applications
§4.44 Other Applications
For applications of generalized exponentials and generalized logarithms to computer arithmetic see §3.1(iv). For an application of the Lambert W -function to generalized Gaussian noise see Chapeau-Blondeau and Monir (2002). For other applications of the Lambert W -function see Corless et al. (1996).
9: 35.9 Applications
§35.9 Applications
See James (1964), Muirhead (1982), Takemura (1984), Farrell (1985), and Chikuse (2003) for extensive treatments. … These references all use results related to the integral formulas (35.4.7) and (35.5.8). For applications of the integral representation (35.5.3) see McFarland and Richards (2001, 2002) (statistical estimation of misclassification probabilities for discriminating between multivariate normal populations). … In the nascent area of applications of zonal polynomials to the limiting probability distributions of symmetric random matrices, one of the most comprehensive accounts is Rains (1998).
10: 7.21 Physical Applications
§7.21 Physical Applications
The error functions, Fresnel integrals, and related functions occur in a variety of physical applications. … Ng and Geller (1969) cites work with applications from atomic physics and astrophysics. … These applications include astrophysics, plasma diagnostics, neutron diffraction, laser spectroscopy, and surface scattering. …