When nu
is large enough, the lower order zeros are incorrect.
besselj_zero(n, 1)
is correct for (integral) nu<52
. But,
julia> besselj_zero(51, 1)
58.16033705734714 # correct
julia> besselj_zero(52, 1)
22.886532747688847 # incorrect
julia> besselj_zero(52, 2)
64.9539962041836 # correct
julia> besselj_zero(66, 2)
79.89174526702548 # correct
julia> besselj_zero(67, 2)
74.79148111822263 # incorrect
This might be fixed by using a bracketed root solver.