# several variables

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## 1—10 of 32 matching pages

##### 1: Bille C. Carlson
Also, the homogeneity of the $R$-function has led to a new type of mean value for several variables, accompanied by various inequalities. …
##### 2: 1.16 Distributions
###### §1.16(vi) Distributions of SeveralVariables
For a multi-index $\boldsymbol{{\alpha}}=(\alpha_{1},\alpha_{2},\dots,\alpha_{n})$, define
1.16.31 $P(\mathbf{x})=\sum_{\boldsymbol{{\alpha}}}c_{\boldsymbol{{\alpha}}}\mathbf{x}^% {\boldsymbol{{\alpha}}}=\sum_{\boldsymbol{{\alpha}}}c_{\boldsymbol{{\alpha}}}x% _{1}^{\alpha_{1}}\cdots x_{n}^{\alpha_{n}},$
1.16.36 $\left\langle\mathscr{F}\left(P(\mathbf{D})u\right),\phi\right\rangle=\left% \langle P_{-}\mathscr{F}\left(u\right),\phi\right\rangle=\left\langle\mathscr{% F}\left(u\right),P_{-}\phi\right\rangle,$
##### 3: 17.12 Bailey Pairs
A sequence of pairs of rational functions of several variables $(\alpha_{n},\beta_{n})$, $n=0,1,2,\dots$, is called a Bailey pair provided that for each $n\geqq 0$
##### 4: 18.37 Classical OP’s in Two or More Variables
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
• J. M. Ortega and W. C. Rheinboldt (1970) Iterative Solution of Nonlinear Equations in Several Variables. Academic Press, New York.
• ##### 6: Bibliography D
• C. F. Dunkl and Y. Xu (2001) Orthogonal Polynomials of Several Variables. Encyclopedia of Mathematics and its Applications, Vol. 81, Cambridge University Press, Cambridge.
• ##### 7: Bibliography S
• C. L. Siegel (1973) 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.
• ##### 8: Bibliography K
• E. G. Kalnins and W. Miller (1993) Orthogonal Polynomials on $n$-spheres: Gegenbauer, Jacobi and Heun. In Topics in Polynomials of One and Several Variables and their Applications, pp. 299–322.
• ##### 9: Bibliography H
• L. K. Hua (1963) Harmonic Analysis of Functions of Several Complex Variables in the Classical Domains. Translations of Mathematical Monographs, Vol. 6, American Mathematical Society, Providence, RI.
• ##### 10: 19.28 Integrals of Elliptic Integrals
To replace a single component of $\mathbf{z}$ in $R_{-a}\left(\mathbf{b};\mathbf{z}\right)$ by several different variables (as in (19.28.6)), see Carlson (1963, (7.9)). …