oscillation of chains
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1—10 of 31 matching pages
1: 10.73 Physical Applications
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§10.73(i) Bessel and Modified Bessel Functions
►Bessel functions first appear in the investigation of a physical problem in Daniel Bernoulli’s analysis of the small oscillations of a uniform heavy flexible chain. … ►In the theory of plates and shells, the oscillations of a circular plate are determined by the differential equation ►
10.73.3
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2: Sidebar 9.SB2: Interference Patterns in Caustics
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►The oscillating intensity of the interference fringes across the caustic is described by the Airy function.
3: 17.17 Physical Applications
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►See Kassel (1995).
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►It involves -generalizations of exponentials and Laguerre polynomials, and has been applied to the problems of the harmonic oscillator and Coulomb potentials.
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4: 6.17 Physical Applications
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►Lebedev (1965) gives an application to electromagnetic theory (radiation of a linear half-wave oscillator), in which sine and cosine integrals are used.
5: 17.12 Bailey Pairs
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►When (17.12.5) is iterated the resulting infinite sequence of Bailey pairs is called a Bailey Chain.
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►The Bailey pair and Bailey chain concepts have been extended considerably.
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6: Bibliography S
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Sturm oscillation and comparison theorems.
In Sturm-Liouville theory,
pp. 29–43.
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An elliptic incarnation of the Bailey chain.
Int. Math. Res. Not. 2002 (37), pp. 1945–1977.
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7: 8.24 Physical Applications
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►The function appears in: discussions of power-law relaxation times in complex physical systems (Sornette (1998)); logarithmic oscillations in relaxation times for proteins (Metzler et al. (1999)); Gaussian orbitals and exponential (Slater) orbitals in quantum chemistry (Shavitt (1963), Shavitt and Karplus (1965)); population biology and ecological systems (Camacho et al. (2002)).
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8: 18.39 Applications in the Physical Sciences
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► a) The Harmonic Oscillator
…Then is the circular
frequency of oscillation (with the ordinary frequency), independent of the amplitude of the oscillations.
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► b) The Morse Oscillator
…The finite system of functions is orthonormal in , see (18.34.7_3).
…The corresponding eigenfunction transform is a generalization of the Kontorovich–Lebedev transform §10.43(v), see Faraut (1982, §IV).
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9: 7.21 Physical Applications
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►Fried and Conte (1961) mentions the role of in the theory of linearized waves or oscillations in a hot plasma; is called the plasma dispersion
function or Faddeeva (or Faddeyeva) function; see Faddeeva and Terent’ev (1954).
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