Timeline for Elliptic Integrals: Mathematica and Gradshteyn and Ryzhik
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
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| Dec 20, 2019 at 8:35 | vote | accept | user91411 | ||
| Dec 19, 2019 at 10:08 | comment | added | bbgodfrey |
Evaluating Chop[s /. vals] with the values of b and c interchanged yields the same numerical value given in my answer above. The same is true, if b and c are interchanged in the numerical integration. This is true for every set of random values I have tried..
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| Dec 19, 2019 at 9:34 | comment | added | user91411 | If the ordering makes no difference, should not the final expression for the integral be symmetric under any permutation of $a, \, b,\, c$ ? Because the integrand has already an exchange symmetry for $a,\, b, \, c$. And yes I meant 3.131 problem #2. | |
| Dec 19, 2019 at 1:22 | comment | added | bbgodfrey |
@user91411 I am confident that the order of a, b, c makes no difference in 3.131 #1. Do you mean 3.13#2 when referring to "the second problem above"?
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| Dec 12, 2019 at 9:34 | comment | added | user91411 | Thanks a lot for the explanation. I feel the relative order of a, b, c must not be overlooked because the integrand has branch cuts. I still don't quite get why we should not get the same answer without having to make the substitution $b\rightarrow c, \,\, c \rightarrow b$. Have you tried to the verify the second problem above ? I ran into similar problem there. Mathematica integrates the second expression alright but the first argument of $F$ turns out to be $\gamma$ instead of $\beta$. | |
| Dec 11, 2019 at 18:34 | history | edited | bbgodfrey | CC BY-SA 4.0 |
improved format
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| Dec 11, 2019 at 17:35 | history | edited | bbgodfrey | CC BY-SA 4.0 |
Major rewrite, taking account of different definitions of F
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| Dec 11, 2019 at 16:28 | history | edited | bbgodfrey | CC BY-SA 4.0 |
provided more recent citation
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| Dec 11, 2019 at 16:08 | history | edited | bbgodfrey | CC BY-SA 4.0 |
fixed typo
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| Dec 11, 2019 at 16:01 | history | answered | bbgodfrey | CC BY-SA 4.0 |