Gaussian
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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
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►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).
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3: 26.21 Tables
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►It also contains a table of Gaussian polynomials up to .
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4: 35.10 Methods of Computation
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►See Yan (1992) for the and functions of matrix argument in the case , and Bingham et al. (1992) for Monte Carlo simulation on applied to a generalization of the integral (35.5.8).
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5: 3.2 Linear Algebra
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§3.2(i) Gaussian Elimination
… ► … ► … ►Iterative Refinement
… ►§3.2(ii) Gaussian Elimination for a Tridiagonal Matrix
…6: 32.14 Combinatorics
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►The distribution function 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 Hermitian matrices; see Tracy and Widom (1994).
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7: 35.9 Applications
§35.9 Applications
…8: 7.1 Special Notation
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►The notations , , and 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
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26.9.4
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►is the Gaussian polynomial (or -binomial coefficient); see also §§17.2(i)–17.2(ii).
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26.9.5
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26.9.6
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26.9.7
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10: 8.24 Physical Applications
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►The function 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)).
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