#2713 taylor of `struve_h' fails

None
open
nobody
5
2014-05-15
2014-03-30
Sergey Litvinov
No

I have this error

(%i1) taylor(struve_h(-1, x), x, 0, 1);
taylor: encountered an unfamiliar singularity in:
struve_h(- 2, x)
 -- an error. To debug this try: debugmode(true);

And this command never returns

taylor(struve_h(-1, x), x, 0, 2);

(%i1) build_info();
(%o1) 
Maxima version: "branch_5_32_base_93_g33a7882"
Maxima build date: "2014-03-27 19:40:19"
Host type: "x86_64-unknown-linux-gnu"
Lisp implementation type: "CLISP"
Lisp implementation version: "2.49 (2010-07-07) (built 3575122160) (memory 3604934424)"

Discussion

  • I've not looked at the second order expansion yet, but the problem with the first example is that we've got a recurrence relation for the derivative of struve_h(v, z) in terms of struve_h(v-1, z). When taylor tries to evaluate the derivative at z=0, it has to evaluate struve_h(-2, 0), which is a pole.

    Of course, struve_h(-1, x) is analytic so this isn't particularly impressive...