[Help-gsl] Underflow in gsl_sf_bessel_Jn_array

[Jonny Taylor]

Please can somebody advise on using gsl_sf_bessel_Jn_array for small z?

I need to generate Bessel functions up to some n_max (of order 50) for  
arbitrary z. I run into problems for small z because the function uses  
a downward recurrence to populate the array, and suffers underflow for  
large n.

It is not a problem for me if underflow occurs at high n: I am  
computing a sum, and if underflow occurs for some n then that will  
definitely not affect the overall result.

What I presume I need to do is to determine what n (<= n_max) I need  
to pass to gsl_sf_bessel_Jn_array in order to avoid underflow.  
Unfortunately that doesn't seem to be trivial to compute (which is not  
really surprising). The best strategies I can come up to are to use a  
lookup which gives the minimum z which works for a given cutoff n, or  
to just try calling gsl_sf_bessel_Jn_e for some trial n and then  
reducing n if I get an error. That is not ideal, though, as I'll need  
to install an error handler and I want to do this in threaded code.

Can anybody suggest a better strategy to take? It seems like this  
should be a relatively simple thing to ask, but I can't come up with a  
simple way of achieving it...

Thanks
Jonny