Use Example 2 and R = 1, so that you get the series

With the zeros α_0,1, α_0,2 · · · from your CAS (see also Table A1 in App. 5).

(a) Graph the terms J₀(α_0,1x), · · ·, J₀(α_0,10x) for 0 ≤ x ≤ 1 on common axes.

(b) Write a program for calculating partial sums of (25). Find out for what f (x) your CAS can evaluate the integrals. Take two such f (x) and comment empirically on the speed of convergence by observing the decrease of the coefficients.

(c) Take f(x) = 1 in (25) and evaluate the integrals for the coefficients analytically by (21a), Sec. 5.4, with v = 1. Graph the first few partial sums on common axes.

Transcribed Image Text:

(25) f(x) = aJo (0,1x) + a Jo (0,2x) + A3J (0,3x) +