Timeline for How to simplify Elliptic integrals?
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
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| Dec 24, 2020 at 5:27 | history | edited | J. M.'s missing motivation♦ |
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| Oct 25, 2020 at 18:26 | history | edited | chris | CC BY-SA 4.0 |
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| Oct 25, 2020 at 12:09 | vote | accept | chris | ||
| Oct 25, 2020 at 12:08 | answer | added | yarchik | timeline score: 7 | |
| Oct 25, 2020 at 6:43 | comment | added | yarchik | See also comments to the answer to this post mathematica.stackexchange.com/questions/204969/… | |
| Oct 25, 2020 at 6:43 | comment | added | yarchik | It turns out that MA can do a lot with elliptic integrals, however, it does not know some identities, in particular Eq.8.126 from Table Of Integrals, Series And Products by Gradshteyn and Ryzhik. I retype them below in original notations $K\!\left(\frac{2\sqrt{k}}{1+k}\right)=(1+k)K(k),$ and $E\!\left(\frac{2\sqrt{k}}{1+k}\right)=\frac1{1+k}\left(2E(k)-(1-k^2)K(k)\right).$ | |
| Oct 24, 2020 at 16:11 | history | edited | chris | CC BY-SA 4.0 |
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| Oct 24, 2020 at 16:01 | comment | added | Michael E2 |
Some evidence, but not complete solution: Series[f2[a] - f1[a], {a, 0, 100}, Assumptions -> {0 < a < 1}] and # == 0 & /@ (f2[a] - f1[a] /. a -> RandomReal[1, 100, WorkingPrecision -> 20]) // Apply[And]
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| Oct 24, 2020 at 15:38 | history | edited | chris | CC BY-SA 4.0 |
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| Oct 24, 2020 at 15:34 | history | asked | chris | CC BY-SA 4.0 |