Airy function cleanup (#18050)

This rearranges the different airy functions, deprecating `airy`, `airyx` and `airyprime` in favour of the more specific variants (`airyai`, `airyaiprime`, etc.), and clarifies the docs of each remaining function. Fixes #17032.

Author: simonbyrne

docs/src/index.md

@@ -517,11 +517,11 @@ asind  acosd  atand  acotd  asecd  acscd
 | [`lbeta(x,y)`](@ref)                                          | accurate `log(beta(x,y))` for large `x` or `y`                                                                                                                  |
 | [`eta(x)`](@ref)                                              | [Dirichlet eta function](https://en.wikipedia.org/wiki/Dirichlet_eta_function) at `x`                                                                           |
 | [`zeta(x)`](@ref)                                             | [Riemann zeta function](https://en.wikipedia.org/wiki/Riemann_zeta_function) at `x`                                                                             |
-| [`airy(z)`](@ref), [`airyai(z)`](@ref), `airy(0,z)`           | [Airy Ai function](https://en.wikipedia.org/wiki/Airy_function) at `z`                                                                                          |
-| [`airyprime(z)`](@ref), [`airyaiprime(z)`](@ref), `airy(1,z)` | derivative of the Airy Ai function at `z`                                                                                                                       |
-| [`airybi(z)`](@ref), `airy(2,z)`                              | [Airy Bi function](https://en.wikipedia.org/wiki/Airy_function) at `z`                                                                                          |
-| [`airybiprime(z)`](@ref), `airy(3,z)`                         | derivative of the Airy Bi function at `z`                                                                                                                       |
-| [`airyx(z)`](@ref), `airyx(k,z)`                              | scaled Airy AI function and `k` th derivatives at `z`                                                                                                           |
+| [`airyai(z)`](@ref)                                           | [Airy Ai function](https://en.wikipedia.org/wiki/Airy_function) at `z`                                                                                          |
+| [`airyaiprime(z)`](@ref)                                      | derivative of the Airy Ai function at `z`                                                                                                                       |
+| [`airybi(z)`](@ref)                                           | [Airy Bi function](https://en.wikipedia.org/wiki/Airy_function) at `z`                                                                                          |
+| [`airybiprime(z)`](@ref)                                      | derivative of the Airy Bi function at `z`                                                                                                                       |
+| [`airyaix(z)`](@ref), [`airyaiprimex(z)`](@ref), [`airybix(z)`](@ref), [`airybiprimex(z)`](@ref) | scaled Airy AI function and `k` th derivatives at `z`                                                                                                           |
 | [`besselj(nu,z)`](@ref)                                       | [Bessel function](https://en.wikipedia.org/wiki/Bessel_function) of the first kind of order `nu` at `z`                                                         |
 | [`besselj0(z)`](@ref)                                         | `besselj(0,z)`                                                                                                                                                  |
 | [`besselj1(z)`](@ref)                                         | `besselj(1,z)`                                                                                                                                                  |