# oscillation of chains

(0.002 seconds)

## 1—10 of 31 matching pages

##### 1: 10.73 Physical Applications

…
►

###### §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
$${\nabla}^{4}W+{\lambda}^{2}\frac{{\partial}^{2}W}{{\partial t}^{2}}=0.$$

…
##### 2: Sidebar 9.SB2: Interference Patterns in Caustics

…
►The oscillating intensity of the interference fringes across the caustic is described by the Airy function.

##### 3: 17.17 Physical Applications

…
►See Kassel (1995).
…
►It involves $q$-generalizations of exponentials and Laguerre polynomials, and has been applied to the problems of the harmonic oscillator and Coulomb potentials.
…

##### 4: 6.17 Physical Applications

…
►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

…
►When (17.12.5) is iterated the resulting infinite sequence of Bailey pairs is called a

*Bailey Chain*. … ►The Bailey pair and Bailey chain concepts have been extended considerably. …##### 6: Bibliography S

…
►
Sturm oscillation and comparison theorems.
In Sturm-Liouville theory,
pp. 29–43.
…
►
An elliptic incarnation of the Bailey chain.
Int. Math. Res. Not. 2002 (37), pp. 1945–1977.
…

##### 7: 8.24 Physical Applications

…
►The function $\gamma (a,x)$ 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)).
…

##### 8: 18.39 Applications in the Physical Sciences

…
► a) The Harmonic Oscillator
…Then $\omega =2\pi \nu =\sqrt{k/m}$ is the

*circular frequency*of oscillation (with $\nu $ the ordinary frequency), independent of the amplitude of the oscillations. … ► b) The Morse Oscillator …The finite system of functions ${\psi}_{n}$ is orthonormal in ${L}^{2}(\mathbb{R},dx)$, see (18.34.7_3). …The corresponding eigenfunction transform is a generalization of the Kontorovich–Lebedev transform §10.43(v), see Faraut (1982, §IV). …##### 9: 7.21 Physical Applications

…
►Fried and Conte (1961) mentions the role of $w\left(z\right)$ in the theory of linearized waves or oscillations in a hot plasma; $w\left(z\right)$ is called the

*plasma dispersion function*or*Faddeeva (or Faddeyeva) function*; see Faddeeva and Terent’ev (1954). …##### 10: 22.19 Physical Applications

…
►