airyx
airyx(k,x)
scaled k
th derivative of the Airy function, return $\operatorname{Ai}(x) e^{\frac{2}{3} x \sqrt{x}}$
for k == 0  k == 1
, and $\operatorname{Ai}(x) e^{ \left \operatorname{Re} \left( \frac{2}{3} x \sqrt{x} \right) \right}$
for k == 2  k == 3
.
Examples
The airyx(k, x)
function in Julia calculates the k
th derivative of the Airy function for a given value x
. The function returns different results based on the value of k
.

Calculate the 0th or 1st derivative of the Airy function:
julia> airy0 = airyx(0, x)
julia> airy1 = airyx(1, x)
When
k
is equal to 0 or 1, the function returnsAi(x) * exp((2/3) * x * sqrt(x))
. 
Calculate the 2nd or 3rd derivative of the Airy function:
julia> airy2 = airyx(2, x)
julia> airy3 = airyx(3, x)
When
k
is equal to 2 or 3, the function returnsAi(x) * exp(abs(Re((2/3) * x * sqrt(x))))
.

Example usage:
julia> x = 1.5; julia> airy0 = airyx(0, x) julia> airy1 = airyx(1, x) julia> airy2 = airyx(2, x) julia> airy3 = airyx(3, x)
This example calculates the 0th, 1st, 2nd, and 3rd derivatives of the Airy function for
x = 1.5
.
See Also
airy, airyai, airyaiprime, airybi, airybiprime, airyprime, airyx,User Contributed Notes
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