Bessel functions of complex argument

[David Lowry-Duda]

On 10:43 Thu 23 Mar 2023, Riccardo Messina wrote:
>I am really new to both MPFR and GMP. My current problem is the 
>evaluation of Bessel functions J and H(1) for complex argument with 
>multiple precision. I have seen the implementation of J in MPFR for 
>real argument but, if I am correct, this function has not been 
>developed in GMP for complex arguments. Could you please confirm to me 
>that this is the case? Do you have any suggestions on how to proceed? I 
>guess that "generalizing" the function defined in MPFR to complex 
>arguments is not that straighforward...

Yes, I think that's correct. But I'll note that Bessel functions are 
implemented in arb

https://arblib.org/arb_hypgeom.html#bessel-functions

and one could translate that back to this scenario.

- DLD