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airyx

airyx(k,x)

scaled kth 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.

1. 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 returns Ai(x) * exp((2/3) * x * sqrt(x)).

2. 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 returns Ai(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.

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