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1: 9.15 Mathematical Applications

… ►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. …

2: DLMF Project News

error generating summary

3: 17.17 Physical Applications

… ►In exactly solved models in statistical mechanics (Baxter (1981, 1982)) the methods and identities of §17.12 play a substantial role. … ►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. …

4: 9.16 Physical Applications

… ►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. … ►Airy functions play a prominent role in problems defined by nonlinear wave equations. …

5: Roelof Koekoek

… ►Koekoek is mainly a teacher of mathematics and has published a few papers on orthogonal polynomials. …

6: René F. Swarttouw

… ►Swarttouw is mainly a teacher of mathematics and has published a few papers on special functions and orthogonal polynomials. …

7: 8.23 Statistical Applications

… ►The function ${\mathrm{B}}_x(a,b)$ and its normalization $I_x(a,b)$ play a similar role in statistics in connection with the beta distribution; see Johnson et al. (1995, pp. 210–275). …

8: 11.2 Definitions

… ►(11.2.11) applies when $x$ is bounded, and (11.2.12) applies when $x$ is bounded away from the origin. … ►(11.2.15) applies when $\left|\mathrm{ph}z\right|\le \pi$ and $z$ is bounded away from the origin. … ►(11.2.17) applies when $|\mathrm{ph}z|\le \frac{1}{2}\pi$ with $z$ bounded away from the origin.

9: Preface

… ►The technical information provided in the Handbook and DLMF was prepared by subject experts from around the world. … ►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. …

10: Michael V. Berry

… ►Berry has published numerous papers on theoretical physics, mainly in quantum mechanics and optics and including the development of associated mathematics, especially asymptotics and geometry. …