######
§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

$W$-function to generalized Gaussian noise see

Chapeau-Blondeau and Monir (2002).
For other

applications of the Lambert

$W$-function see

Corless et al. (1996).

######
§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.
…