Gaussian elimination

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1: 35.7 Gaussian Hypergeometric Function of Matrix Argument

§35.7 Gaussian Hypergeometric Function of Matrix Argument

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§35.7(i) Definition

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Jacobi Form

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Confluent Form

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Integral Representation

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2: 3.2 Linear Algebra

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§3.2(i) Gaussian Elimination

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Iterative Refinement

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§3.2(ii) Gaussian Elimination for a Tridiagonal Matrix

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3: 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). …

4: 26.21 Tables

… ►It also contains a table of Gaussian polynomials up to ${\left[\genfrac{}{}{0.0pt}{}{12}{6}\right]}_q$. …

5: 35.10 Methods of Computation

… ►See Yan (1992) for the ${}_1{}^{}F_1^{}$ and ${}_2{}^{}F_1^{}$ 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). …

6: 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 $n\times n$ Hermitian matrices; see Tracy and Widom (1994). …

7: 35.9 Applications

§35.9 Applications

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8: Bille C. Carlson

… ►The main theme of Carlson’s mathematical research has been to expose previously hidden permutation symmetries that can eliminate a set of transformations and thereby replace many formulas by a few. …

9: 7.1 Special Notation

… ►The notations $P(z)$, $Q(z)$, and $\mathrm{\Phi }(z)$ are used in mathematical statistics, where these functions are called the normal or Gaussian probability functions.

10: 4.43 Cubic Equations

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