Timeline for Is there any alternative for NSolve or Solve to obtain all the roots of the given function?
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| Oct 2, 2021 at 18:38 | comment | added | bbgodfrey |
@math2021 NSolve is seeking values of x for which f is approximately, not exactly, equal to zero. Incidentally, Simplify[f /. x -> (2 n - 1) Pi/(2 n), n > 1 && n \[Element] Integers] spits out several error messages but finally yields 0. Probably, when it encounters an error, it tries a different order of simplification.
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| Oct 2, 2021 at 17:49 | comment | added | math2021 | So, does this mean that Mathematica is providing the roots that the function is not defined at those values? These points are also visible in the plots. @bbgodfrey | |
| Oct 2, 2021 at 17:49 | comment | added | math2021 |
Thanks, the problem is that it can be easily checked that all the roots these methods give are rational multiples of $\pi$. x={1/2, 3/4, 5/6, 7/8, 9/10, 11/12, 13/14, 15/16, 17/18, 19/20, 21/ 22} \[Pi] , on the other hand, if you check the function at these values, you see that the function is not defined at all at these values since at these values, the argument of $\csc \left(\frac{\pi ^2}{\pi -x}\right)$ will be integer multiples of $\pi$. @bbgodfrey
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| Oct 2, 2021 at 14:00 | history | answered | bbgodfrey | CC BY-SA 4.0 |