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1: 35.7 Gaussian Hypergeometric Function of Matrix Argument
§35.7 Gaussian Hypergeometric Function of Matrix Argument
§35.7(i) Definition
Jacobi Form
Confluent Form
Integral Representation
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). …
3: 26.21 Tables
It also contains a table of Gaussian polynomials up to [ 12 6 ] q . …
4: 35.10 Methods of Computation
See Yan (1992) for the F 1 1 and F 1 2 functions of matrix argument in the case m = 2 , and Bingham et al. (1992) for Monte Carlo simulation on O ( m ) applied to a generalization of the integral (35.5.8). …
5: 32.14 Combinatorics
The distribution function F ( s ) given by (32.14.2) arises in random matrix theory where it gives the limiting distribution for the normalized largest eigenvalue in the Gaussian Unitary Ensemble of n × n Hermitian matrices; see Tracy and Widom (1994). …
6: 3.2 Linear Algebra
§3.2(i) Gaussian Elimination
Iterative Refinement
§3.2(ii) Gaussian Elimination for a Tridiagonal Matrix
7: 35.9 Applications
§35.9 Applications
8: 7.1 Special Notation
The notations P ( z ) , Q ( z ) , and Φ ( z ) are used in mathematical statistics, where these functions are called the normal or Gaussian probability functions.
9: 26.9 Integer Partitions: Restricted Number and Part Size
26.9.4 [ m n ] q = j = 1 n 1 - q m - n + j 1 - q j , n 0 ,
is the Gaussian polynomial (or q -binomial coefficient); see also §§17.2(i)17.2(ii). …
26.9.5 n = 0 p k ( n ) q n = j = 1 k 1 1 - q j = 1 + m = 1 [ k + m - 1 m ] q q m ,
10: 8.24 Physical Applications
The function γ ( 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)). …