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closed form for regular superfunction expressed as a periodic function
#2
(08/27/2010, 02:09 PM)sheldonison Wrote: .... Perhaps there is a closed form limit equation for the other a_n terms in the periodic series?
- Sheldon
Originally, I intended to solve it mathematically, with limit equations of some sort, but I gave up. Anyway, I brute forced the numerical solutions using complex Fourier analysis, and the results looked good.



I suspect a_3 would be the reciprical of a polynomial in L, L^2, but I wasn't able to find the pattern... yet. I will continue to pursue both limit equations, and numerical results .... Here are the numerical results. This would provide another way of calculating the regular superfunction.
0.318131505204764 + 1.33723570143069*I
1.00000000000000 - 2.60599763775608 E-46*I
-0.151314897155652 - 0.296748836732241*I
-0.0369763094090676 + 0.0987305443114970*I
0.0258115979731401 - 0.0173869621265308*I
-0.00794441960244236 + 0.000579250181689956*I
0.00197153171916544 + 0.000838273147502224*I
-0.000392010935257457 - 0.000393133164925080*I
0.0000581917506305269 + 0.000119532747356117*I
-0.00000315362731515909 - 0.0000302507270044311*I
-0.00000144282204032780 + 0.00000712739202459367*I
0.000000659214290634412 - 0.00000152248373494640*I
-0.000000194922185012021 + 0.000000284379660774925*I
0.0000000534780813335645 - 0.0000000461525820619042*I
-0.0000000140401213835816 + 0.00000000762603302713942*I
0.00000000315342989238929 - 0.00000000146720737059747*I
-0.000000000591418449135739 + 0.000000000254860555536866*I
1.07938974205158 E-10 - 2.18783515598918 E-11*I
-2.47877770137887 E-11 - 1.92092983484722 E-12*I
6.07224941506231 E-12 + 1.28233399551471 E-13*I
-1.11638719710692 E-12 + 2.71214581539618 E-13*I
1.27498904804777 E-13 - 5.65381557065319 E-14*I
-1.63566889526104 E-14 - 9.67900985098162 E-15*I
7.43073077006837 E-15 + 4.93269953498429 E-15*I
-2.43590387189014 E-15 - 5.21055989895944 E-17*I
3.19983418022330 E-16 - 3.06533506041410 E-16*I
2.35111634696870 E-17 + 4.77456396407459 E-17*I
-7.31502044718856 E-18 + 1.10974529579819 E-17*I
-3.26221285971496 E-18 - 3.99734388033735 E-18*I
1.39071827030212 E-18 - 2.43545980631280 E-19*I
-8.14762787710817 E-20 + 3.02121739652423 E-19*I
-5.68424637170392 E-20 - 3.30544545268232 E-20*I
1.00134634420191 E-20 - 1.20846493207443 E-20*I
2.44040335072592 E-21 + 3.32815768651263 E-21*I
-1.00281770980843 E-21 + 3.16126717352352 E-22*I
7.46727364275524 E-24 - 2.52461237780373 E-22*I
5.59031612947253 E-23 + 1.92941756355972 E-23*I
-8.03434017691000 E-24 + 1.15003875138068 E-23*I
-2.13560370410329 E-24 - 2.64275348521218 E-24*I
7.66352536099374 E-25 - 3.06816449234638 E-25*I
1.42509561746275 E-26 + 1.97884314138339 E-25*I
-4.58748818093499 E-26 - 1.10298477574201 E-26*I
5.73983689586017 E-27 - 9.59735542776205 E-27*I
1.77067703342646 E-27 + 1.97743801995778 E-27*I
-5.74269137934548 E-28 + 2.60660071774678 E-28*I
-1.76277133832552 E-29 - 1.48518580873011 E-28*I
3.46938198356513 E-29 + 6.74672128662828 E-30*I
-4.01277862515764 E-30 + 7.29505202539481 E-30*I
-1.34399669008111 E-30 - 1.42300404827861 E-30*I
4.14782554384895 E-31 - 1.97836607707266 E-31*I


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Messages In This Thread
RE: regular superfunction expressed as a periodic function - by sheldonison - 08/28/2010, 08:44 PM

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