Hankel functions sometimes throw NaN values

[olaca09]

I recently bumped into hankelh1() and hankelh2() returning NaN real parts for nu = 7, x= \sqrt(15^2-1). Values close to this point both in nu and x behave nicely. Is besseljy() behaving badly here for whatever reason?

julia> import SpecialFunctions
julia> import Bessels
julia> x = sqrt(15^2 - 1);
julia> SpecialFunctions.besselh(7, 1, x)
0.028099885144514142 - 0.21733228481429356im

julia> Bessels.hankelh1(7, x)
NaN - 0.2173322848142936im

Perhaps I'll try some troubleshooting myself soon, but I figured I'd make sure I'm not misunderstanding something simple here.

[heltonmc]

No this is indeed a bug! Thank you for the report. What is happening is in the continued fraction

Bessels.jl/src/BesselFunctions/hankel.jl

Line 175 in 17aa052

d = inv(b - d)

at these specific values b=d causing infinities to propagate through and return NaN