Timeline for radius of convergence for taylor series in mathematica
Current License: CC BY-SA 4.0
19 events
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| Feb 26, 2020 at 18:03 | comment | added | user62716 | Thank you march.. | |
| Feb 26, 2020 at 17:57 | comment | added | march | @user62716. I mean, that material is standard fare for undergraduate mathematics courses. I expect that it would be in a lot of standard undergraduate calculus texts. | |
| Feb 26, 2020 at 17:51 | comment | added | user62716 | Thanks it works now!!! can you suggest some good book or lecture notes for series, radius of convergence, Taylor series | |
| Feb 26, 2020 at 17:47 | comment | added | march |
@user62716. Because in the definition of tbl, there is an a[n] rather than Cos[n], left over from how I coded it in my copy of Mathematica. I have fixed it, and you should fix your definition of tbl and rerun the code.
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| Feb 26, 2020 at 17:47 | history | edited | march | CC BY-SA 4.0 |
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| Feb 26, 2020 at 17:46 | comment | added | user62716 | Dear march, the last line Table[Max[tbl[[;; kk]]], {kk, 1, 10000}] // ListPlot is not work I don't know why? | |
| Feb 26, 2020 at 17:44 | vote | accept | user62716 | ||
| Feb 26, 2020 at 17:29 | history | edited | march | CC BY-SA 4.0 |
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| Feb 26, 2020 at 17:28 | comment | added | march |
@Artes. Okay! Thank you! I haven't played much with the analytic Sum features in Mathematica. It's irritating that I couldn't get SumConvergence to make this work. So it goes. Of course, it seems to me that the OP wasn't really clear on what they wanted anyway.
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| Feb 26, 2020 at 17:24 | comment | added | Artes |
@march Sum[Cos[n] x^n, {n, 1, Infinity}, VerifyConvergence -> True, GenerateConditions -> True]
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| Feb 26, 2020 at 17:20 | comment | added | march |
@Artes. Well, sure! But since SumConvergence doesn't work, we can't get the radius of convergence directly or analytically. Hence my answer. (Am I missing something?)
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| Feb 26, 2020 at 17:10 | comment | added | march | @Artes. I'd forgotten about that one. Unfortunately, it doesn't seem to work for the example I've written up in my edited answer! | |
| Feb 26, 2020 at 17:09 | history | edited | march | CC BY-SA 4.0 |
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| Feb 26, 2020 at 17:00 | comment | added | Artes |
@user62716 What you are looking form is just SumConvergence, it has options where one can use e.g. "IntegralTest", "RaabeTest","RatioTest", however there is no tool which can predict another coefficient of a series you have in mind.
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| Feb 26, 2020 at 16:57 | comment | added | march | But those aren't series, those are just polynomials. Unless you have a general expression for the (infinite number of) coefficients, then all you have are polynomials, and so the radius of convergence is of course always infinite. | |
| Feb 26, 2020 at 16:55 | comment | added | user62716 | I modified the question, I want general way for any series, can we do it? | |
| Feb 26, 2020 at 16:52 | comment | added | march | @user62716. Perhaps give an example of a more complicated series and edit your OP with your true question! | |
| Feb 26, 2020 at 16:51 | comment | added | user62716 | Thank you march, since it simple coefficients you can find it but for complicate series what shall we do for: 0.1 + 0.397953 t + 0.592849 t^2 + 0.588719 t^3 + 0.438295 t^4 + 0.260863 t^5 + 0.129195 t^6 | |
| Feb 26, 2020 at 16:47 | history | answered | march | CC BY-SA 4.0 |