One solution to the Bessel equation of (nonnegative) integer order N...

One solution to the Bessel equation of (nonnegative) integer order N

(a) Write the first three terms of J₀(x).

(b) Let J(0, x,m) denote the mth partial sum

Plot J(0, x, 4) and use your plot to approximate the first positive zero of J₀(x). Compare your value against a tabulated value or one generated by a computer algebra system.

(c) Plot J₀(x) and J(0, x, 4) on the same axes over the interval [0, 2]. How well do they compare?

(d) If your system has built-in Bessel functions, plot J₀(x) and J(0, x,m) on the same axes over the interval [0, 10] for various values of m. What is the smallest value of m that gives an accurate approximation to the first three positive zeros of J₀(x)?