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AiryAi, AiryBi - The Airy Ai and Bi wave functions
Calling Sequence
AiryAi(x)
AiryBi(x)
AiryAi(n, x)
AiryBi(n, x)
Parameters
n
-
algebraic expression (the order or index)
x
algebraic expression (the argument)
Description
The Airy wave functions AiryAi and AiryBi are linearly independent solutions for w in the equation . Specifically,
where 0F1 is the generalized hypergeometric function, and .
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 is the 3rd derivative of evaluated at , and not the 3rd derivative of .
The Airy functions are related to Bessel functions of order for (see the examples below).
Examples
See Also
AiryZeros, Bessel, convert[Airy], convert[Bessel], initialfunctions
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