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

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      https://www.ias.ac.in/article/fulltext/reso/026/05/0629-0647

    • Keywords

       

      Airy and Bairy functions, Fourier transform, contour integration, numerical techniques.

    • Abstract

       

      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 be-ginning 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 ob-tain these functions.

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