return sequence of bessel functions

[baptiste]

I'm very new to julia, so not sure I managed to find the actual source code being used for those bessel(jhy) functions. There's a related thread suggesting that the chosen algorithm for integer arguments is different.

Nonetheless, for the general case, the Amos implementation returns a sequence of bessel functions, nu+I-1, I=1,...,N, and it would be very nice if the julia wrapper could return the whole sequence. Currently, I believe julia implements vectorisation over nu as a for loop and just takes the one value from the Amos sequence (or openlibm's).
Since it is not uncommon to need a sequence of values (Bessel functions tend to be used in recurrence relations), it is a bit wasteful to iterate over nu when it was already done at the Fortran level.

Related question on StackOverflow

[tkelman]

It looks like we only ever call zbesj with N=1, see

julia/base/special/bessel.jl

Lines 144 to 150 in 400fa31

	function _besselj(nu::Float64, z::Complex128, kode::Int32)
	ccall((:zbesj_,openspecfun), Void,
	(Ptr{Float64}, Ptr{Float64}, Ptr{Float64}, Ptr{Int32}, Ptr{Int32},
	Ptr{Float64}, Ptr{Float64}, Ptr{Int32}, Ptr{Int32}),
	&real(z), &imag(z), &nu, &kode, &1,
	pointer(cy,1), pointer(cy,2),
	pointer(ae,1), pointer(ae,2))

- you should however be able to do a slightly different ccall yourself if you would like a larger N.

You may also find it neat/useful that Amos was translated to Julia here: https://github.com/nolta/SpecialFunctions.jl
We should probably replace the Fortran part of openspecfun with that at some point (#8536), just haven't yet done the work of turning that into a full-fledged tested and registered Julia package.

[IainNZ]

(thanks for filing this @baptiste!)

[KristofferC]

Moved to JuliaMath/SpecialFunctions.jl#26