scipy.special.jn_zeros

scipy.special.jn_zeros(n, nt)[source]

Compute zeros of integer-order Bessel functions Jn.

Compute nt zeros of the Bessel 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 \(n > 0\).

Parameters
nint

Order of Bessel function

ntint

Number of zeros to return

Returns
ndarray

First nt zeros of the Bessel function.

See also

jv

References

1

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

Examples

>>> import scipy.special as sc

We can check that we are getting approximations of the zeros by evaluating them with jv.

>>> n = 1
>>> x = sc.jn_zeros(n, 3)
>>> x
array([ 3.83170597,  7.01558667, 10.17346814])
>>> sc.jv(n, x)
array([-0.00000000e+00,  1.72975330e-16,  2.89157291e-16])

Note that the zero at x = 0 for n > 0 is not included.

>>> sc.jv(1, 0)
0.0