Timeline for Real roots of an infinite series consisting of Harmonic number
Current License: CC BY-SA 4.0
7 events
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| Jan 21, 2021 at 20:26 | comment | added | Michael E2 |
@Farhad If you start FindRoot at a point where the function doesn't return a number, FindRoot will quit. So your starting point has to be a value of s for which the series converges.
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| Jan 21, 2021 at 19:35 | comment | added | Ferhat | Thank you all. It means that the starting point has to be in the convergence radius??? I did not know the logic behind it. @ user64494 @ Michael E2 | |
| Jan 21, 2021 at 18:47 | comment | added | user64494 |
FindRoot[(Exp[s^2] (1 - r))/r - 1 == Sum[Exp[s (1 - s) HarmonicNumber[n]], {n, 1, \[Infinity]}], {s, -2}] finds it. When RealAbs[s] is big, then there is no real root there.
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| Jan 21, 2021 at 18:31 | history | edited | Michael E2 | CC BY-SA 4.0 |
Responded to comment
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| Jan 21, 2021 at 18:27 | comment | added | Michael E2 |
Yeah, you get convergence for s less than the conjugate of the golden section, too. I guess my focus locked in on the OP's code and the problem with it. Thanks.
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| Jan 21, 2021 at 18:19 | comment | added | user64494 |
Another real root is s == -1.21830031520808.
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| Jan 21, 2021 at 17:58 | history | answered | Michael E2 | CC BY-SA 4.0 |