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Airy functions and applications to physics. 2nd ed. (English) Zbl 1207.33010
Hackensack, NJ: World Scientific (ISBN 978-1-84816-548-9/hbk). x, 202 p. $ 70.00; £ 43.00 (2010).

The book gives a survey of diverse properties and applications of Airy functions.

Every chapter of the book contains exercises. Chapter 1 gives a historical introduction. Chapter 2 is about definitions and various properties like zeros and asymptotic expansions. Chapter 3 contains primitive functions. Chapter 4 treats Airy transforms and various transforms of Airy functions. Chapter 5 gives a brief introduction to oscillating integrals and its application to second order differential equations. Chapter 6 gives some generalizations of Airy functions. In chapter 7 applications to classical physics are given. Chapter 8 treats applications to quantum physics. Numerical computation of the Airy functions is described briefly in the Appendix A.

MSC:
33C10Bessel and Airy functions, cylinder functions, 0 F 1
33-02Research monographs (special functions)
33C90Applications of hypergeometric functions