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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. … Λ : 𝒟 ( I ) is called a distribution if it is a continuous linear functional on 𝒟 ( I ) , that is, it is a linear functional and for every ϕ n ϕ in 𝒟 ( I ) , … (See the definition of a distribution in §1.16(i).) …
1.16.35 ( u ) , ϕ = u , ( ϕ ) , ϕ 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
complex plane (excluding infinity).
equals by definition.
3: 26.2 Basic Definitions
§26.2 Basic Definitions
Lattice Path
4: 7.2 Definitions
§7.2 Definitions
§7.2(i) Error Functions
§7.2(ii) Dawson’s Integral
§7.2(iii) Fresnel Integrals
§7.2(v) Goodwin–Staton Integral
5: 4.2 Definitions
§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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  • 7: 4.14 Definitions and Periodicity
    §4.14 Definitions and Periodicity
    8: 34.6 Definition: 9 j Symbol
    §34.6 Definition: 9 j Symbol
    9: 26.5 Lattice Paths: Catalan Numbers
    §26.5(i) Definitions
    (Sixty-six equivalent definitions of C ( n ) are given in Stanley (1999, pp. 219–229).) …
    10: 5.2 Definitions
    §5.2 Definitions
    Euler’s Integral