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Zbl 1207.33010
Vallée, Olivier; Soares, Manuel
Airy functions and applications to physics. 2nd ed. (English)
[B] Hackensack, NJ: World Scientific. x, 202~p. \$~70.00; \sterling~43.00 (2010). ISBN 978-1-84816-548-9/hbk

The book gives a survey of diverse properties and applications of Airy functions.\par 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.
[Juri M. Rappoport (Moskva)]

MSC 2000:: *33C10 Cylinder functions, etc.
33-02 Research monographs (special functions)
33C90 Appl. of hypergeometric functions

Keywords: Airy function; physics; Bessel function; asymptotic expansions; oscillating integral

Citations: Zbl 1056.33006

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