# Roots of Bessel function

Since SpecialFunctions.jl doesn't have a method to calculate roots of Bessel function, we implemented approx_besselroots.

approx_besselroots(ν::Real, n::Integer) -> Vector{Float64}

Return the first $n$ roots of Bessel function. Note that this function is only 12-digits of precision.

$$$J_{\nu}(x) = \sum_{m=0}^{\infty}\frac{(-1)^j}{\Gamma(\nu+j+1)j!} \left(\frac{x}{2}\right)^{2j+\nu}$$$

Examples

julia> ν = 0.3;

julia> roots = approx_besselroots(ν, 10);

julia> zeros = (x -> besselj(ν, x)).(roots);

julia> all(zeros .< 1e-12)
true
source

This method approx_besselroots is used to calculate gaussjacobi and gausslaguerre.