Could I use complex arguments in the algorithms for computing Bessel functions of integer order? Of course, extending the operators +,-,*,/ and the functions sin, cos, exp, log, square root, etc and changing absolute value by modulus. If so, Could I have an idea of the figures of accuracy?

I apologize about my English, but, as you can see, it’s not my mother tongue.

Hi, Andres (sorry I don't know how to type the accent in your name!)

No, in general what you propose won't work. The NR routines for Bessel functions of integer order use a combination of recurrence and rational function approximation. For arbitrary complex arguments, the recurrences *might* be unstable, and the rational function approximations are almost *sure* to be bad.

You might do better with the NR routines for Bessel functions of fractional order -- just because these use continued fractions, which are more likely to converge. However they also use recurrences, so I think that this would be very hard to get to work.

One source for the algorithm that you need might be SLATEC, available at Netlib (http://www.netlib.org) If you look at the table of contents at http://www.netlib.org/slatec/toc under section C10A4, you'll see that there's a routine that claims to do what you want.

The bad news, perhaps, is that it is in Fortran -- real old Fortran!

Hope this helps!

Thank you very much.

I'll have to clean the dust on my -- real old Fortran, but this information can take me out of a dead end road. ;)

Thanks a lot.