scipy.special.jnp_zeros¶

scipy.special.jnp_zeros(n, nt)[source]¶

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 \(n > 1\).

Parameters

nint: Order of Bessel function
ntint: Number of zeros to return

Returns

ndarray: First n zeros of the Bessel function.

See also

jvp, 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 jvp.

>>> 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 = 0 for n > 1 is not included.

>>> sc.jvp(n, 0)
0.0

scipy.special.jn_zeros scipy.special.yn_zeros