|
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,
|
![AiryAi(z)=c[1] `0F1`( ; (2)/(3); ((z)^(3))/(9))-c[2] z `0F1`( ; (4)/(3); ((z)^(3))/(9))](/support/helpjp/helpview.aspx?si=4723/file00004/math73.png)
![AiryBi(z)=(3)^((1)/(2)) [c[1] `0F1`( ; (2)/(3); ((z)^(3))/(9))+c[2] z `0F1`( ; (4)/(3); ((z)^(3))/(9))]](/support/helpjp/helpview.aspx?si=4723/file00004/math78.png)
|
|
where 0F1 is the generalized hypergeometric function, ![c[1] = AiryAi(0)](/support/helpjp/helpview.aspx?si=4723/file00004/math83.png) and ![c[2] = -(D(AiryAi))(0)](/support/helpjp/helpview.aspx?si=4723/file00004/math85.png) .
|
|
•
|
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.
|
|
•
|
The Airy functions are related to Bessel functions of order  for  (see the examples below).
|
|
|
|
Examples
|
|
|
>
|
|
|
| (1) |
|
>
|
|
|
| (2) |
|
>
|
|
|
| (3) |
|
>
|
|
|
| (4) |
|
>
|
|
|
| (5) |
|
>
|
|
|
| (6) |
|
>
|
|
|
| (7) |
|
>
|
|
|
| (8) |
|
>
|
|
|
| (9) |
|
>
|
|
|
| (10) |
|
>
|
|
|
| (11) |
|
>
|
|
|
| (12) |
|
|
Download Help Document
Was this information helpful?
