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1: 8.19 Generalized Exponential Integral
§8.19 Generalized Exponential Integral
§8.19(ii) Graphics
§8.19(ix) Inequalities
§8.19(x) Integrals
§8.19(xi) Further Generalizations
2: 16.2 Definition and Analytic Properties
§16.2(i) Generalized Hypergeometric Series
Note also that any partial sum of the generalized hypergeometric series can be represented as a generalized hypergeometric function via …
§16.2(v) Behavior with Respect to Parameters
3: 8.21 Generalized Sine and Cosine Integrals
§8.21 Generalized Sine and Cosine Integrals
§8.21(i) Definitions: General Values
§8.21(iv) Interrelations
§8.21(v) Special Values
4: 1.16 Distributions
Λ : 𝒟 ( I ) is called a distribution, or generalized function, 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 ) , … More generally, for α : [ a , b ] [ , ] a nondecreasing function the corresponding Lebesgue–Stieltjes measure μ α (see §1.4(v)) can be considered as a distribution: … More generally, if α ( x ) is an infinitely differentiable function, then … Friedman (1990) gives an overview of generalized functions and their relation to distributions. …
5: 35.8 Generalized Hypergeometric Functions of Matrix Argument
§35.8 Generalized Hypergeometric Functions of Matrix Argument
§35.8(i) Definition
Convergence Properties
§35.8(iv) General Properties
6: 19.2 Definitions
§19.2(i) General Elliptic Integrals
7: 8.16 Generalizations
§8.16 Generalizations
For a generalization of the incomplete gamma function, including asymptotic approximations, see Chaudhry and Zubair (1994, 2001) and Chaudhry et al. (1996). Other generalizations are considered in Guthmann (1991) and Paris (2003).
8: 17.15 Generalizations
§17.15 Generalizations
9: 7.16 Generalized Error Functions
§7.16 Generalized Error Functions
Generalizations of the error function and Dawson’s integral are 0 x e t p d t and 0 x e t p d t . …
10: 16.26 Approximations
§16.26 Approximations
For discussions of the approximation of generalized hypergeometric functions and the Meijer G -function in terms of polynomials, rational functions, and Chebyshev polynomials see Luke (1975, §§5.12 - 5.13) and Luke (1977b, Chapters 1 and 9).