The Airy Ai and Bi wave functions
algebraic expression (the order or index)
algebraic expression (the argument)
The Airy wave functions AiryAi and AiryBi are linearly independent solutions for w in the equation w''⁢−z⁢w=0. Specifically,
where F10 is the generalized hypergeometric function, c1=AiryAi⁡0 and c2=−AiryAi'⁡0.
The two argument forms are used to represent the derivatives, so AiryAi(1, x) = D(AiryAi)(x) and AiryBi(1, x) = D(AiryBi)(x). Note that all higher derivatives can be written in terms of the 0'th and 1st derivatives.
Note also that AiryAi⁡3,x2 is the 3rd derivative of AiryAi⁡x evaluated at x2, and not the 3rd derivative of AiryAi⁡x2.
The Airy functions are related to Bessel functions of order n3 for n=−2,−1,1,2 (see the examples below).
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