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1: 9.15 Mathematical Applications
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►Airy functions play an indispensable role in the construction of uniform asymptotic expansions for contour integrals with coalescing saddle points, and for solutions of linear second-order ordinary differential equations with a simple turning point.
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2: 17.17 Physical Applications
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►In exactly solved models in statistical mechanics (Baxter (1981, 1982)) the methods and identities of §17.12 play a substantial role.
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►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.
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3: 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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►Airy functions play a prominent role in problems defined by nonlinear wave equations.
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4: 8.23 Statistical Applications
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►The function and its normalization
play a similar role in statistics in connection with the beta distribution; see Johnson et al. (1995, pp. 210–275).
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5: Preface
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►The technical information provided in the Handbook and DLMF was prepared by subject experts from around the world.
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►The validators played a critical role in the project, one that was absent in its 1964 counterpart: to provide critical, independent reviews during the development of each chapter, with attention to accuracy and appropriateness of subject coverage.
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6: 15.17 Mathematical Applications
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►Hypergeometric functions, especially complete elliptic integrals, also play an important role in quasiconformal mapping.
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7: 16.24 Physical Applications
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►The symbols, or Clebsch–Gordan coefficients, play an important role in the decomposition of reducible representations of the rotation group into irreducible representations.
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8: 7.20 Mathematical Applications
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►The complementary error function also plays a ubiquitous role in constructing exponentially-improved asymptotic expansions and providing a smooth interpretation of the Stokes phenomenon; see §§2.11(iii) and 2.11(iv).
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9: 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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10: 8.22 Mathematical Applications
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►plays a fundamental role in re-expansions of remainder terms in asymptotic expansions, including exponentially-improved expansions and a smooth interpretation of the Stokes phenomenon.
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