Kelvin ship-wave pattern
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11: 10.69 Uniform Asymptotic Expansions for Large Order
§10.69 Uniform Asymptotic Expansions for Large Order
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10.69.2
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►All fractional powers take their principal values.
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12: 10.71 Integrals
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§10.71(i) Indefinite Integrals
… ►§10.71(ii) Definite Integrals
… ►§10.71(iii) Compendia
►For infinite double integrals involving Kelvin functions see Prudnikov et al. (1986b, pp. 630–631). … ►13: 11.8 Analogs to Kelvin Functions
§11.8 Analogs to Kelvin Functions
…14: 10.66 Expansions in Series of Bessel Functions
15: 10.68 Modulus and Phase Functions
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►Equations (10.68.8)–(10.68.14) also hold with the symbols , , , and replaced throughout by , , , and , respectively.
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§10.68(i) Definitions
… ►§10.68(ii) Basic Properties
… ►§10.68(iii) Asymptotic Expansions for Large Argument
…16: Sidebar 9.SB2: Interference Patterns in Caustics
Sidebar 9.SB2: Interference Patterns in Caustics
…17: Sidebar 21.SB1: Periodic Surface Waves
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►The caption reads “Mosaic of two overhead photographs, showing surface patterns of waves in shallow water”.
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18: 10.76 Approximations
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Kelvin Functions
…19: Sidebar 7.SB1: Diffraction from a Straightedge
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►The faint circular patterns are additional diffraction effects due to imperfections in the edge.
20: 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 , , , .
…For the Kelvin functions the order is always assumed to be real.
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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).