Airy Functions Demystified — I The Mathematical Physics of an Innocent Looking Differential Equation — Basics and Numerical Solutions

Airy functions have been long important in various areas of mathematics, physics, and astronomy. Even though the Airy differential equation looks extremely simple, its solutions are generally ‘notorious’ in nature. In this expository article, we have given a thorough description of the Airy function...

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Bibliographic Details
Published inResonance Vol. 26; no. 5; pp. 629 - 647
Main Authors Ramkarthik, M. S., Pereira, Elizabeth Louis
Format Journal Article
LanguageEnglish
Published New Delhi Springer India 01.05.2021
Subjects
Education
General Article
Humanities and Social Sciences
multidisciplinary
Science
Science Education
Fourier transform
contour integration
Airy and Bairy functions
numerical techniques
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Summary:Airy functions have been long important in various areas of mathematics, physics, and astronomy. Even though the Airy differential equation looks extremely simple, its solutions are generally ‘notorious’ in nature. In this expository article, we have given a thorough description of the Airy functions with real arguments. Majority of the books (with the exception of specialized books on the subject) do not pay attention in detail to these functions. Taking this as a motivating factor, we have written this article for postgraduates and students beginning research to help them understand the nitty-gritty of these beautiful functions. The solutions of the Airy differential equation called the Airy and Bairy functions are explained in detail. Finally, we have given some ideas to numerically obtain these functions.
ISSN:0971-8044
0973-712X
DOI:10.1007/s12045-021-1166-4