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11: 20 Theta Functions
Chapter 20 Theta Functions
…12: 13.28 Physical Applications
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►For potentials in quantum mechanics that are solvable in terms of confluent hypergeometric functions see Negro et al. (2000).
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13: Bibliography I
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The real roots of Bernoulli polynomials.
Ann. Univ. Turku. Ser. A I 37, pp. 1–20.
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An electrostatics model for zeros of general orthogonal polynomials.
Pacific J. Math. 193 (2), pp. 355–369.
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More on electrostatic models for zeros of orthogonal polynomials.
Numer. Funct. Anal. Optim. 21 (1-2), pp. 191–204.
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14: 19.35 Other Applications
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§19.35(ii) Physical
►Elliptic integrals appear in lattice models of critical phenomena (Guttmann and Prellberg (1993)); theories of layered materials (Parkinson (1969)); fluid dynamics (Kida (1981)); string theory (Arutyunov and Staudacher (2004)); astrophysics (Dexter and Agol (2009)). …15: 16.24 Physical Applications
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§16.24(i) Random Walks
… ►They are also potentially useful for the solution of more complicated restricted lattice walk problems, and the 3D Ising model; see Barber and Ninham (1970, pp. 147–148). …16: 9.16 Physical Applications
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►Again, the quest for asymptotic approximations that are uniformly valid solutions to this equation in the neighborhoods of critical points leads (after choosing solvable equations with similar asymptotic properties) to Airy functions.
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17: 16.23 Mathematical Applications
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►These equations are frequently solvable in terms of generalized hypergeometric functions, and the monodromy of generalized hypergeometric functions plays an important role in describing properties of the solutions.
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18: Sidebar 22.SB1: Decay of a Soliton in a Bose–Einstein Condensate
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►Jacobian elliptic functions arise as solutions to certain nonlinear Schrödinger equations, which model many types of wave propagation phenomena.
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19: Robb J. Muirhead
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►Muirhead’s main research interests are multivariate statistical analysis, statistical modeling, Bayesian statistics, and pharmaceutical statistics.
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20: Ian J. Thompson
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► 1953 in New Zealand) has been since 2006 a Theoretical Nuclear Physicist in the Nuclear Theory and Modeling Group of the Lawrence Livermore National Laboratory, Livermore, California.
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