§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.
…
§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.
§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).
§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).
§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
-function to generalized Gaussian noise see
Chapeau-Blondeau and Monir (2002).
For other
applications of the Lambert
-function see
Corless et al. (1996).
§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).
§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.
…
