I originally posted this question @ Reconciling roots of a series However, I got no responses. I have done further work on the problem & attempted to delete my original posting to initiate this one. I did not see the option to delete Reconciling roots of a series. So if any website moderator can delete the original & leave this one stand that would be helpful. The results in this posting are more illuminating.
I have an infinite series that is function of
/2 Pi k x\
\ T / where k is the frequency parameter that is an integer value from 1 to m. The series is also linearly dependent on the coefficient, Ck. However, Ck is nonlinear with respect to k. 3 other parameters are undefined, a0, N, & tau. Taking the derivative of the series removes the constant a0 & the factor (2 Pi k)/T comes out of the sin term & the sin term bcomes a cos term. N is a positive integer & tau is a real #, generally between 0 & 1.
The derivative of the series can be evaluated since Ck falls of by 1/k^2 which renders the factor (2 Pi k)/T to (2 Pi)/T. All is well & MAPLE seems to confirm that by the result (5). I then attempt to find the roots of the derivative after defining the values for m, a0, N, & tau with both the solve & RootFinding:-Analytic commands. The results from the 2 do not seem to coincide.
I then repeat the process with chek2. Now there seems to be some overlap in the results. But as I pointed out in Reconciling roots of a series in the case of chek the series parameters m, a0, N, & tau have not been assigned values. In the case of chek2 those parameters do have assigned values; hence, the solution characteristics are different for the solve command, but not for RootFinding:-Analytic.
In a different problem, but somewhat related someone pointed out the superior computational performance of the RootFinding:-Analytic as opposed to the solve command. The results here if I interpret them correctly suggest that the solve command can be WRONG altogether. Can this be explained in a concise & coherent manner that most users can follow? Also, solve can produce an analytic expression as opposed the RootFinding:-Analytic command. Is there a way to use the RootFinding package to produce an analytical result? In the case presented below I suppose the analytic result for solutions to chek would be JUNK?