There are four varieties of Airy functions: Ai(z), Bi(z), Gi(z), and Hi(z). Of these, Ai(z) and Bi(z) are by far the most common, with Gi(z) and Hi(z) being encountered much less frequently. Airy functions commonly appear in physics, especially in optics, quantum mechanics, electromagnetics, and radiative transfer. Ai(z) and Bi(z) are entire functions. A generalization of the Airy function was constructed by Hardy. The Airy function Ai(x) and Bi(x) functions are plotted above along the real axis.
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