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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: 26.2 Basic Definitions
§26.2 Basic Definitions
Permutation
Lattice Path
Partition
3: 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
4: 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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  • 6: 4.14 Definitions and Periodicity
    §4.14 Definitions and Periodicity
    7: 34.6 Definition: 9 j Symbol
    §34.6 Definition: 9 j Symbol
    8: 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).) …
    9: 5.2 Definitions
    §5.2 Definitions
    Euler’s Integral
    10: 18.3 Definitions
    §18.3 Definitions
    Table 18.3.1 provides the definitions of Jacobi, Laguerre, and Hermite polynomials via orthogonality and normalization (§§18.2(i) and 18.2(iii)). …
    Table 18.3.1: Orthogonality properties for classical OP’s: intervals, weight functions, normalizations, leading coefficients, and parameter constraints. …
    Name p n ( x ) ( a , b ) w ( x ) h n k n k ~ n / k n Constraints
    Note that in this reference the definitions of the Chebyshev polynomials of the third and fourth kinds V n ( x ) and W n ( x ) are the converse of the definitions in this chapter. …