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1: 34.4 Definition: Symbol
§34.4 Definition: Symbol
►The symbol is defined by the following double sum of products of symbols: … ►The symbol can be expressed as the finite sum … ►where is defined as in §16.2. ►For alternative expressions for the symbol, written either as a finite sum or as other terminating generalized hypergeometric series of unit argument, see Varshalovich et al. (1988, §§9.2.1, 9.2.3).2: 8.19 Generalized Exponential Integral
§8.19 Generalized Exponential Integral
… ►For an extensive treatment of see Chapter 6. … ►§8.19(ii) Graphics
… ►§8.19(ix) Inequalities
… ►§8.19(xi) Further Generalizations
…3: 16.2 Definition and Analytic Properties
…
►
§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
…4: 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
… ►5: 1.16 Distributions
…
►
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 ,
…
►More generally, for a nondecreasing function the corresponding Lebesgue–Stieltjes measure (see §1.4(v)) can be considered as a distribution:
…
►More generally, if is an infinitely differentiable function, then
…
►Friedman (1990) gives an overview of generalized functions and their relation to distributions.
…
6: 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
…7: 6 Exponential, Logarithmic, Sine, and
Cosine Integrals
Chapter 6 Exponential, Logarithmic, Sine, and Cosine Integrals
…8: 23 Weierstrass Elliptic and Modular
Functions
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