Hankel%20loop%20integral
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1: 10.1 Special Notation
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►The main functions treated in this chapter are the Bessel functions , ; Hankel functions , ; modified Bessel functions , ; spherical Bessel functions , , , ; modified spherical Bessel functions , , ; Kelvin functions , , , .
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►Abramowitz and Stegun (1964): , , , , for , , , , respectively, when .
►Jeffreys and Jeffreys (1956): for , for , for .
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►For older notations see British Association for the Advancement of Science (1937, pp. xix–xx) and Watson (1944, Chapters 1–3).
2: 1.14 Integral Transforms
§1.14 Integral Transforms
… ►where the last integral denotes the Cauchy principal value (1.4.25). … ►If is absolutely integrable on for every finite , and the integral (1.14.47) converges, then … ►§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).3: 8.19 Generalized Exponential Integral
§8.19 Generalized Exponential Integral
►§8.19(i) Definition and Integral Representations
… ►Other Integral Representations
… ►§8.19(ii) Graphics
… ►§8.19(x) Integrals
…4: 6.2 Definitions and Interrelations
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§6.2(i) Exponential and Logarithmic Integrals
… ► … ►The logarithmic integral is defined by … ►§6.2(ii) Sine and Cosine Integrals
… ► …5: 8.21 Generalized Sine and Cosine Integrals
§8.21 Generalized Sine and Cosine Integrals
… ►§8.21(iii) Integral Representations
… ►§8.21(iv) Interrelations
… ►§8.21(v) Special Values
… ►6: 7.2 Definitions
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§7.2(ii) Dawson’s Integral
… ►§7.2(iii) Fresnel Integrals
… ►Values at Infinity
… ►§7.2(iv) Auxiliary Functions
… ►§7.2(v) Goodwin–Staton Integral
…7: 7.18 Repeated Integrals of the Complementary Error Function
§7.18 Repeated Integrals of the Complementary Error Function
►§7.18(i) Definition
… ►§7.18(iii) Properties
… ► … ►Hermite Polynomials
…8: 19.16 Definitions
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