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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
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►
§16.2(i) Generalized Hypergeometric Series
… ► … ►Polynomials
… ►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
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►
is called a distribution, or generalized function, if it is a continuous linear functional on , that is, it is a linear functional and for every in ,
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►More generally, for a nondecreasing function the corresponding Lebesgue–Stieltjes measure (see §1.4(v)) can be considered as a distribution:
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►More generally, if is an infinitely differentiable function, then
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►Friedman (1990) gives an overview of generalized functions and their relation to distributions.
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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
… ►Confluence
…6: 19.2 Definitions
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§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 and . …10: Foreword
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►The online version, the NIST Digital
Library of Mathematical Functions (DLMF), presents the same technical information along with extensions and innovative interactive features consistent with the new medium.
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►Particular attention is called to the generous support of the National Science Foundation, which made possible the participation of experts from academia and research institutes worldwide.
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