How can I make definite integral to Bessel function in the interval from 0 to infinite

i used the commend 'guadgk' to make definite integral to Bessel function in the interval from 0 to infinite, the result turns out to be that it's not a good way to solve it.

the code:

clc;
clear;
f=@(q)BESSELJ(0,q);
n=quadgk(f,0,inf)

the result displayed in the commend window:

Warning: Reached the limit on the maximum number of intervals in use.
Approximate bound on error is 1.0e+007. The integral may not exist, or
it may be difficult to approximate numerically. Increase MaxIntervalCount
to 712 to enable QUADGK to continue for another iteration. 
> In quadgk>vadapt at 317
  In quadgk at 216
  In test_4 at 4

n =

    1.3759e+007

what should i do ?

Answer 1

[Mike Hosea]

I'm not sure I understand the problem. The answer is 1, so use 1 instead of quadgk(f,0,inf). However, if you are concerned about the results over a finite range of 0 to b, I would not be concerned unless b is large. The improper integral of f, or the integral over a large interval, is just one of those problems that needs to be approached analytically or with a highly specialized numerical method tailored in some sense to that particular problem.