Roots of bessel function of first kind for negative n in Matlab

Question

There are some codes which compute the roots of

J_n(x),    n > 0

I want to calculate the roots of:

J_n(x),    n < 0

n is a real number.

Is there some algorithm or yet better some Matlab code which does this.

Have you tried `fzero`? How many of the roots do you want? What particular values/range of `n`? — horchler, Jan 12 '16 at 15:26
If n is restricted to the Integers, the functions have the same roots since they're linear dependent to a factor of (-1)^n. — TroyHaskin, Jan 12 '16 at 15:39

score 0 · Answer 1 · answered Jan 12 '16 at 17:23

In this paper there is an algorithm to calculate the N first roots of Bessel function of the first kind. This works only if n > -1 in J_n(x).

The whole root calculation turns into an eigenvalue problem. The estimated errors have been calculated in the paper.

1 Answers1