Airy functions and applications to physics

by Vallée, Olivier

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Title Statements

Full title :Airy functions and applications to physics / Olivier Vallée, Manuel Soares.

Edition Statements

Publication Date:©2010
Edition:2nd ed

Publication Statements

Publisher(s):Imperial College Press
Place of Publication:Singapore
Language:eng
Publication Date:©2010

Notes

4.3.3 Fourier transform of Airy functions

The Physical Object

Description:1 online resource (213 pages)

Edition Identifiers

ISBN:9781848165502, 1848165501
oclc:on1108522269
LC Classification:QA351
Dewey Decimal:515.55

Intro; Contents; Preface; 1. A Historical Introduction: Sir George Biddell Airy; 2. Definitions and Properties; 2.1 Homogeneous Airy functions; 2.1.1 The Airy equation; 2.1.2 Elementary properties; 2.1.2.1 Wronskians of homogeneous Airy functions; 2.1.2.2 Particular values of Airy functions; 2.1.2.3 Relations between Airy functions; 2.1.3 Integral representations; 2.1.4 Ascending and asymptotic series; 2.1.4.1 Expansion of Ai near the origin; 2.1.4.2 Ascending series of Ai and Bi; 2.1.4.3 Asymptotic expansion of Ai and Bi; 2.1.4.4 The Stokes phenomenon; 2.2 Properties of Airy functions

2.2.1 Zeros of Airy functions2.2.2 The spectral zeta function; 2.2.3 Inequalities; 2.2.4 Connection with Bessel functions; 2.2.5 Modulus and phase of Airy functions; 2.2.5.1 Definitions; 2.2.5.2 Differential equations; 2.2.5.3 Asymptotic expansions; 2.2.5.4 Functions of positive arguments; 2.3 Inhomogeneous Airy functions; 2.3.1 Definitions; 2.3.2 Properties of inhomogeneous Airy functions; 2.3.2.1 Values at the origin; 2.3.2.2 Other integral representations; 2.3.3 Ascending series and asymptotic expansion; 2.3.3.1 Ascending series; 2.3.3.2 Asymptotic expansions

2.3.4 Zeros of the Scorer functions…