When the index ν is real, the functions J_ν(z), J_ν^, (z), Y_ν(z), and Y_ν^, (z) each have an infinite number of real zeros, all of which are simple with the possible exception of z = 0. For nonnegative ν, the kth positive zeros of these functions are denoted j_(ν, k), j_(ν, k)^, , y_(ν, k), and y_(ν, k)^, , respectively, except that z = 0 is typically counted as the first zero of J_0^, (z). The first few roots j_(n, k) of the Bessel function J_n(x) are given in the following table for small nonnegative integer values of n and k. They can be found in the Wolfram Language using the command BesselJZero[n, k].

Bessel function | Bessel function of the first kind