I submitted this PR a little too early. All tests ran successfully on my machine where Int === Int64, but I see some have failed in CI on x86 machines, where Int === Int32, and the @test_broken tests are actually no longer broken. I also now see from the comments preceding the "high nu" test set that Issue #27 is a duplicate of Issue #10. I'll modify this PR to replace the @test_broken tests to @test after which I think everything should work ok.

Edit: Changing this to a WIP (Work In Progress) PR since the problem still occurs for even higher nu values. Please don't merge yet.

Ok, I've implemented an asymptotic formula from DLMF that is appropriate for large nu and small n. Now the first three zeros of any of the four treated functions are returned correctly for any positive nu value. All zeros are returned correctly for nu less than or equal to 93.

Here is an example of finding the correct first three zeros for a high-order Bessel function:

julia> using FunctionZeros, SpecialFunctions, Plots

julia> t = [bessely_deriv_zero(500, n) for n in 1:3]
3-element Vector{Float64}:
 514.5723799304565
 526.0501131866687
 535.4459280973557

julia> bessely_deriv(nu, x) = 0.5 * (bessely(nu-1, x) - bessely(nu+1, x))
bessely_deriv (generic function with 1 method)

julia> bessely_deriv.(500, t)
3-element Vector{Float64}:
 -2.6506574712925612e-15
  6.893097204141441e-14
 -2.5673907444456745e-16

julia> plot(range(500, 550, 100), x -> bessely_deriv(500, x)); scatter!(t, zeros(length(t)))

• Removed WIP from title of PR.
• Please review