integrals of vector-valued functions
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1: 1.14 Integral Transforms
§1.14 Integral Transforms
… ►where the last integral denotes the Cauchy principal value (1.4.25). … ►If is integrable on for all in , then the integral (1.14.32) converges and is an analytic function of in the vertical strip . … ►§1.14(viii) Compendia
►For more extensive tables of the integral transforms of this section and tables of other integral transforms, see Erdélyi et al. (1954a, b), Gradshteyn and Ryzhik (2000), Marichev (1983), Oberhettinger (1972, 1974, 1990), Oberhettinger and Badii (1973), Oberhettinger and Higgins (1961), Prudnikov et al. (1986a, b, 1990, 1992a, 1992b).2: 7.2 Definitions
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§7.2(i) Error Functions
… ►§7.2(ii) Dawson’s Integral
… ►§7.2(iii) Fresnel Integrals
… ► , , and are entire functions of , as are and in the next subsection. … ►§7.2(iv) Auxiliary Functions
…3: 7.18 Repeated Integrals of the Complementary Error Function
§7.18 Repeated Integrals of the Complementary Error Function
… ► … ►Hermite Polynomials
… ►Confluent Hypergeometric Functions
… ►Parabolic Cylinder Functions
…4: 19.16 Definitions
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§19.16(i) Symmetric Integrals
… ►Just as the elementary function (§19.2(iv)) is the degenerate case … ►§19.16(ii)
►All elliptic integrals of the form (19.2.3) and many multiple integrals, including (19.23.6) and (19.23.6_5), are special cases of a multivariate hypergeometric function …The -function is often used to make a unified statement of a property of several elliptic integrals. …5: 8.19 Generalized Exponential Integral
§8.19 Generalized Exponential Integral
►§8.19(i) Definition and Integral Representations
… ►Other Integral Representations
… ►§8.19(vi) Relation to Confluent Hypergeometric Function
… ►§8.19(x) Integrals
…6: 6.2 Definitions and Interrelations
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