application to Rossby waves
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11: 24.18 Physical Applications
§24.18 Physical Applications
… ►Euler polynomials also appear in statistical physics as well as in semi-classical approximations to quantum probability distributions (Ballentine and McRae (1998)).12: 4.44 Other Applications
§4.44 Other Applications
… ►For applications of generalized exponentials and generalized logarithms to computer arithmetic see §3.1(iv). ►For an application of the Lambert -function to generalized Gaussian noise see Chapeau-Blondeau and Monir (2002). For other applications of the Lambert -function see Corless et al. (1996).13: 9.16 Physical Applications
§9.16 Physical Applications
… ►An application of Airy functions to the solution of this equation is given in Gramtcheff (1981). … ►Reference to many of these applications as well as to the theory of elasticity and to the heat equation are given in Vallée and Soares (2010): a book devoted specifically to the Airy and Scorer functions and their applications in physics. … ►This reference provides several examples of applications to problems in quantum mechanics in which Airy functions give uniform asymptotic approximations, valid in the neighborhood of a turning point. … ►An application of the Scorer functions is to the problem of the uniform loading of infinite plates (Rothman (1954b, a)).14: 35.9 Applications
§35.9 Applications
… ►See James (1964), Muirhead (1982), Takemura (1984), Farrell (1985), and Chikuse (2003) for extensive treatments. … ►These references all use results related to the integral formulas (35.4.7) and (35.5.8). ►For applications of the integral representation (35.5.3) see McFarland and Richards (2001, 2002) (statistical estimation of misclassification probabilities for discriminating between multivariate normal populations). … ►In the nascent area of applications of zonal polynomials to the limiting probability distributions of symmetric random matrices, one of the most comprehensive accounts is Rains (1998).15: 36.14 Other Physical Applications
§36.14 Other Physical Applications
►§36.14(i) Caustics
… ►§36.14(ii) Optics
… ►§36.14(iv) Acoustics
►Applications include the reflection of ultrasound pulses, and acoustical waveguides. …16: 17.17 Physical Applications
§17.17 Physical Applications
… ►They were given this name because they play a role in quantum physics analogous to the role of Lie groups and special functions in classical mechanics. See Kassel (1995). … ►It involves -generalizations of exponentials and Laguerre polynomials, and has been applied to the problems of the harmonic oscillator and Coulomb potentials. …17: 19.35 Other Applications
18: 13.27 Mathematical Applications
§13.27 Mathematical Applications
… ►The other group elements correspond to integral operators whose kernels can be expressed in terms of Whittaker functions. … ►For applications of Whittaker functions to the uniform asymptotic theory of differential equations with a coalescing turning point and simple pole see §§2.8(vi) and 18.15(i).19: 36 Integrals with Coalescing Saddles
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