Timeline for How to calculate the infinite sum of this double series?
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| Dec 11, 2014 at 12:34 | comment | added | Hjalmar Rosengren | Sounds very interesting. I'm not surprised that elliptic functions are useful for this kind of physical problem. The formula for the potential in your link also seems directly related to elliptic functions. | |
| Dec 11, 2014 at 11:40 | comment | added | tcya | Thank you. The answer goes much deeper than I expected. It's actually a special case of Thompson-Lampard theorem in electrodynamics. That's why Griffiths knew the answer though he couldn't prove it for this specific case. Maybe by making other special cases we can get some results for similar infinite series, but both the theorem and the theta function are beyond my current knowledge. If interested, you may refer to the solutions here link for 3.47 and 3.48a for Thompson-Lampard theorem. | |
| Dec 10, 2014 at 9:09 | history | answered | Hjalmar Rosengren | CC BY-SA 3.0 |