§16.24 Physical Applications
Contents
§16.24(i) Random Walks
Generalized hypergeometric functions and Appell functions appear in the evaluation of the so-called Watson integrals which characterize the simplest possible lattice walks. They are also potentially useful for the solution of more complicated restricted lattice walk problems, and the 3D Ising model; see Barber and Ninham (1970, pp. 147–148).
§16.24(ii) Loop Integrals in Feynman Diagrams
Appell functions are used for the evaluation of one-loop integrals in Feynman diagrams. See Cabral-Rosetti and Sanchis-Lozano (2000).
For an extension to two-loop integrals see Moch et al. (2002).
§16.24(iii) 
, 
, and 
Symbols
- Keywords:
-
Clebsch–Gordan coefficients, angular momentum, generalized hypergeometric functions, relation to generalized hypergeometric functions, relations to other functions,
symbols
- Permalink:
- http://dlmf.nist.gov/16.24.iii
- See also:
- Annotations for §16.24 and Ch.16
The symbols, or Clebsch–Gordan coefficients, play an important role in the
decomposition of reducible representations of the rotation group into
irreducible representations. They can be expressed as 
functions with unit argument. The coefficients of transformations between
different coupling schemes of three angular momenta are related to the Wigner
symbols. These are balanced 
functions with unit argument.
Lastly, special cases of the symbols are 
functions
with unit argument. For further information see Chapter 34 and
Varshalovich et al. (1988, §§8.2.5, 8.8, and 9.2.3).
