Timeline for Integrate$[\frac{\cos(x-y)\cos(5y)}{C+\cos(m-y)+B\cos(x-y)},y]$ results in massive, unusable expression. Can it be simplified?
Current License: CC BY-SA 3.0
6 events
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| Mar 6, 2017 at 22:13 | comment | added | sonicboom | @ThiesHeidecke This integral arose when analyzing a frequency bandgap problem in a 2D periodic crystal..it is part of a very complicated eigenvalue calculation. $m$ and $x$ are both in $[0, 2 \pi)$. I actually need to evaluate the definite integral from $y = 0$ to $2 \pi$. I posted it as an indefinite integral as I thought it might be simpler to obtain that. I need a usable closed form expression for this integral as it is needed to develop other components of the larger eigenvalue problem. | |
| Mar 6, 2017 at 20:49 | comment | added | Julien Kluge | Applying the Assuming-Option as suggested by Thies Heidecke and Simplifiyng afterwards with the Assumptions leads to a formula which is 'only' one page long (after about 15min evaluation time). | |
| Mar 6, 2017 at 20:04 | history | edited | Thies Heidecke | CC BY-SA 3.0 |
Edited LaTeX formatting in title
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| Mar 6, 2017 at 19:51 | comment | added | Thies Heidecke |
What problem are you solving with this? Or in other words, what's your application for the solution? Do you really need the indefinite integral or are you using it for definite integrals? What is the domain of m? As a general tip, you can use Assumptions -> {-1/2 < B < 0, C > 1} as an option to Integrate though in this case it won't solve your problem of a too big output.
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| Mar 6, 2017 at 19:41 | review | First posts | |||
| Mar 6, 2017 at 19:50 | |||||
| Mar 6, 2017 at 19:38 | history | asked | sonicboom | CC BY-SA 3.0 |