When nu is large enough, the root finding fails.

When nu is large enough, the root finding fails.

(@v1.12) pkg> st FunctionZeros
Status `~/.julia/environments/v1.12/Project.toml`
  [b21f74c0] FunctionZeros v1.1.0

julia> besselj_
besselj_deriv_zero
besselj_zero
julia> besselj_zero(73.5, 2)
ERROR: DomainError with -57.89075833371584:
`x` must be nonnegative.
Stacktrace:
  [1] besselj(nu::Float64, x::Float64)
    @ SpecialFunctions ~/.julia/packages/SpecialFunctions/6nmlv/src/bessel.jl:527
  [2] #_besselj_zero##0
    @ ~/.julia/packages/FunctionZeros/aNQPA/src/FunctionZeros.jl:93 [inlined]
  [3] Callable_Function
    @ ~/.julia/packages/Roots/odaES/src/functions.jl:29 [inlined]
  [4] update_state
    @ ~/.julia/packages/Roots/odaES/src/DerivativeFree/secant.jl:39 [inlined]
  [5] update_state
    @ ~/.julia/packages/Roots/odaES/src/DerivativeFree/secant.jl:29 [inlined]
  [6] solve!(𝐙::Roots.ZeroProblemIterator{Roots.Secant, Roots.AlefeldPotraShi, Roots.Callable_Function{…}, Roots.UnivariateZeroState{…}, Roots.UnivariateZeroOptions{…}, Roots.NullTracks}; verbose::Bool)
    @ Roots ~/.julia/packages/Roots/odaES/src/hybrid.jl:54
  [7] solve!
    @ ~/.julia/packages/Roots/odaES/src/hybrid.jl:30 [inlined]
  [8] solve(𝑭𝑿::Roots.ZeroProblem{FunctionZeros.var"#_besselj_zero##0#_besselj_zero##1"{Float64}, Float64}, M::Roots.Order0, p::Nothing; verbose::Bool, kwargs::@Kwargs{tracks::Roots.NullTracks})
    @ Roots ~/.julia/packages/Roots/odaES/src/find_zero.jl:498
  [9] solve
    @ ~/.julia/packages/Roots/odaES/src/find_zero.jl:490 [inlined]
 [10] #find_zero#40
    @ ~/.julia/packages/Roots/odaES/src/find_zero.jl:220 [inlined]
 [11] find_zero (repeats 2 times)
    @ ~/.julia/packages/Roots/odaES/src/find_zero.jl:210 [inlined]
 [12] find_zero
    @ ~/.julia/packages/Roots/odaES/src/find_zero.jl:243 [inlined]
 [13] _besselj_zero
    @ ~/.julia/packages/FunctionZeros/aNQPA/src/FunctionZeros.jl:92 [inlined]
 [14] besselj_zero(nu::Float64, n::Int64)
    @ FunctionZeros ~/.julia/packages/FunctionZeros/aNQPA/src/FunctionZeros.jl:117
 [15] top-level scope
    @ REPL[6]:1
Some type information was truncated. Use `show(err)` to see complete types.

This is fixed in the pending PR #28 as shown below:

julia> using Pkg: Pkg

julia> Pkg.activate(temp=true)
  Activating new project at `C:\Users\peter\AppData\Local\Temp\jl_FCgDwf`

julia> Pkg.add(url="https://github.com/simonp0420/FunctionZeros.jl", rev="fix_overflow")
    Updating git-repo `https://github.com/simonp0420/FunctionZeros.jl`
   Resolving package versions...
    Updating `C:\Users\peter\AppData\Local\Temp\jl_FCgDwf\Project.toml`
  [b21f74c0] + FunctionZeros v1.1.0 `https://github.com/simonp0420/FunctionZeros.jl#fix_overflow`
    Updating `C:\Users\peter\AppData\Local\Temp\jl_FCgDwf\Manifest.toml`
  [7d9f7c33] + Accessors v0.1.43
  [38540f10] + CommonSolve v0.2.4
  [a33af91c] + CompositionsBase v0.1.2
  [187b0558] + ConstructionBase v1.6.0
  [ffbed154] + DocStringExtensions v0.9.5
  [b21f74c0] + FunctionZeros v1.1.0 `https://github.com/simonp0420/FunctionZeros.jl#fix_overflow`
  [3587e190] + InverseFunctions v0.1.17
  [92d709cd] + IrrationalConstants v0.2.6
  [692b3bcd] + JLLWrappers v1.7.1
  [2ab3a3ac] + LogExpFunctions v0.3.29
  [1914dd2f] + MacroTools v0.5.16
  [21216c6a] + Preferences v1.5.1 [loaded: v1.5.0]
  [f2b01f46] + Roots v2.2.10
  [276daf66] + SpecialFunctions v2.6.1
  [efe28fd5] + OpenSpecFun_jll v0.5.6+0
  [56f22d72] + Artifacts v1.11.0
  [ade2ca70] + Dates v1.11.0
  [8f399da3] + Libdl v1.11.0
  [37e2e46d] + LinearAlgebra v1.12.0
  [de0858da] + Printf v1.11.0
  [fa267f1f] + TOML v1.0.3
  [4ec0a83e] + Unicode v1.11.0
  [e66e0078] + CompilerSupportLibraries_jll v1.3.0+1
  [4536629a] + OpenBLAS_jll v0.3.29+0
  [05823500] + OpenLibm_jll v0.8.7+0
  [8e850b90] + libblastrampoline_jll v5.15.0+0

julia> Pkg.add("SpecialFunctions")
   Resolving package versions...
    Updating `C:\Users\peter\AppData\Local\Temp\jl_FCgDwf\Project.toml`
  [276daf66] + SpecialFunctions v2.6.1
    Manifest No packages added to or removed from `C:\Users\peter\AppData\Local\Temp\jl_FCgDwf\Manifest.toml`

julia> using FunctionZeros: besselj_zero

julia> using SpecialFunctions: besselj

julia> x = besselj_zero(73.5, 2)
87.8434178096031

julia> besselj(x, 2)
1.0754863847166907e-134

Great! I will close this issue after your PR is merged.

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When nu is large enough, the root finding fails. #29

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When nu is large enough, the root finding fails. #29

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simonp0420 commented on Dec 25, 2025

zhaiyusci commented on Dec 31, 2025

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