# definition

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##### 1: 1.16 Distributions
The linear space of all test functions with the above definition of convergence is called a test function space. … $\Lambda:\mathcal{D}(I)\rightarrow\mathbb{C}$ is called a distribution if it is a continuous linear functional on $\mathcal{D}(I)$, that is, it is a linear functional and for every $\phi_{n}\to\phi$ in $\mathcal{D}(I)$, … (See the definition of a distribution in §1.16(i).) …
1.16.35 $\left\langle\mathscr{F}\left(u\right),\phi\right\rangle=\left\langle u,% \mathscr{F}(\phi)\right\rangle,$ $\phi\in\mathcal{T}_{n}$.
##### 2: Mathematical Introduction
These include, for example, multivalued functions of complex variables, for which new definitions of branch points and principal values are supplied (§§1.10(vi), 4.2(i)); the Dirac delta (or delta function), which is introduced in a more readily comprehensible way for mathematicians (§1.17); numerically satisfactory solutions of differential and difference equations (§§2.7(iv), 2.9(i)); and numerical analysis for complex variables (Chapter 3). …
###### Common Notations and Definitions
 $\mathbb{C}$ complex plane (excluding infinity). … equals by definition. …
##### 5: 4.2 Definitions
###### §4.2(i) The Logarithm
With this definition the general logarithm is given by … We regard this as the closed definition of the principal value. … In contrast to (4.2.5) the closed definition is symmetric. …
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##### 8: 34.6 Definition: $\mathit{9j}$ Symbol
###### §34.6 Definition: $\mathit{9j}$ Symbol
(Sixty-six equivalent definitions of $C\left(n\right)$ are given in Stanley (1999, pp. 219–229).) …