# several variables

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## 1—10 of 32 matching pages

##### 1: Bille C. Carlson

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►Also, the homogeneity of the $R$-function has led to a new type of mean value for several variables, accompanied by various inequalities.
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##### 2: 1.16 Distributions

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###### §1.16(vi) Distributions of Several Variables

… ►For a multi-index $\mathit{\alpha}=({\alpha}_{1},{\alpha}_{2},\mathrm{\dots},{\alpha}_{n})$, define ►
1.16.31
$$P(\mathbf{x})=\sum _{\mathit{\alpha}}{c}_{\mathit{\alpha}}{\mathbf{x}}^{\mathit{\alpha}}=\sum _{\mathit{\alpha}}{c}_{\mathit{\alpha}}{x}_{1}^{{\alpha}_{1}}\mathrm{\cdots}{x}_{n}^{{\alpha}_{n}},$$

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1.16.36
$$\u27e8\mathcal{F}\left(P(\mathbf{D})u\right),\varphi \u27e9=\u27e8{P}_{-}\mathcal{F}\left(u\right),\varphi \u27e9=\u27e8\mathcal{F}\left(u\right),{P}_{-}\varphi \u27e9,$$

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##### 3: 17.12 Bailey Pairs

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►A sequence of pairs of rational functions of several variables
$({\alpha}_{n},{\beta}_{n})$, $n=0,1,2,\mathrm{\dots}$, is called a

*Bailey pair*provided that for each $n\geqq 0$ …##### 4: 18.37 Classical OP’s in Two or More Variables

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►Orthogonal polynomials associated with root systems are certain systems of trigonometric polynomials in several variables, symmetric under a certain finite group (Weyl group), and orthogonal on a torus.
…In several variables they occur, for $q=1$, as

*Jack polynomials*and also as*Jacobi polynomials associated with root systems*; see Macdonald (1995, Chapter VI, §10), Stanley (1989), Kuznetsov and Sahi (2006, Part 1), Heckman (1991). …##### 5: Bibliography O

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Iterative Solution of Nonlinear Equations in Several Variables.
Academic Press, New York.
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##### 6: Bibliography D

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Orthogonal Polynomials of Several Variables.
Encyclopedia of Mathematics and its Applications, Vol. 81, Cambridge University Press, Cambridge.
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##### 7: Bibliography S

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Topics in Complex Function Theory. Vol. III: Abelian Functions and Modular Functions of Several Variables.
Interscience Tracts in Pure and Applied Mathematics, No. 25, Wiley-Interscience, [John Wiley & Sons, Inc], New York-London-Sydney.
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##### 8: Bibliography K

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Orthogonal Polynomials on $n$-spheres: Gegenbauer, Jacobi and Heun.
In Topics in Polynomials of One and Several Variables and their
Applications,
pp. 299–322.
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##### 9: Bibliography H

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Harmonic Analysis of Functions of Several Complex Variables in the Classical Domains.
Translations of Mathematical Monographs, Vol. 6, American Mathematical Society, Providence, RI.
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