Compute zeros of integer-order Bessel function derivatives Jn’.
Compute nt zeros of the functions \(J_n'(x)\) on the interval \((0, \infty)\). The zeros are returned in ascending order. Note that this interval excludes the zero at \(x = 0\) that exists for \(n > 1\).
Order of Bessel function
Number of zeros to return
First n zeros of the Bessel function.
Zhang, Shanjie and Jin, Jianming. “Computation of Special Functions”, John Wiley and Sons, 1996, chapter 5. https://people.sc.fsu.edu/~jburkardt/f_src/special_functions/special_functions.html
>>> import scipy.special as sc
We can check that we are getting approximations of the zeros by evaluating them with
>>> n = 2 >>> x = sc.jnp_zeros(n, 3) >>> x array([3.05423693, 6.70613319, 9.96946782]) >>> sc.jvp(n, x) array([ 2.77555756e-17, 2.08166817e-16, -3.01841885e-16])
Note that the zero at
x = 0for
n > 1is not included.
>>> sc.jvp(n, 0) 0.0