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 the extent of generalization Gottfried Ultimate Fellow Posts: 853 Threads: 126 Joined: Aug 2007 10/14/2007, 06:31 PM (This post was last modified: 10/14/2007, 07:46 PM by Gottfried.) The matrix, analytically constructed based on the hypothese, that the eigenvalues are the consecutive powers of u = log(t) $\hspace{24} \begin{matrix} {rrr} 1.00000000000 & 1.00000000000 & 1.00000000000 \\ 0 & 1.57079632679*I & 3.14159265359*I \\ 0 & -1.23370055014 & -4.93480220054 \\ 0 & -0.645964097506*I & -5.16771278005*I \\ 0 & 0.253669507901 & 4.05871212642 \\ 0 & 0.0796926262462*I & 2.55016403988*I \\ 0 & -0.0208634807634 & -1.33526276886-2.13383011501E-12*I \\ 0 & -0.00468175413532*I & 9.74997503272E-12-0.599264529316*I \\ 0 & 0.000919260274839 & 0.235330630320+1.03824464497E-11*I \\ 0 & 0.000160441184787*I & 7.34062412572E-11+0.0821458865076*I \\ 0 & -0.0000252020423730 & -0.0258068913636+0.000000000336008212438*I \\ 0 & -0.00000359884323522*I & -0.000000000531166859357-0.00737043148889*I \\ 0 & 0.000000471087478009 & 0.00192957576096+1.44905471842E-10*I \\ 0 & 0.0000000569217294451*I & -0.00000000197293927481+0.000466304152891*I \\ 0 & -0.00000000638660319694 & -0.000104637211800-0.00000000321239246183*I \\ 0 & -0.000000000668803312296*I & 0.00000000165543902983-0.0000219117619420*I \\ 0 & 6.56592442263E-11 & 0.00000429946860414-0.00000000166180488357*I \\ 0 & 6.06668588155E-12*I & 0.00000000320792169496+0.000000794286619384*I \\ 0 & -1.00000000000E-12 & -0.000000140053803989+0.00000000195676397990*I \\ 0 & 0 & -2.05225455659E-10-0.0000000242612901612*I \\ 0 & 0 & 0.00000000407962123588+0.000000000376346155829*I \\ 0 & 0 & -2.13051400732E-10+0.000000000561705712732*I \\ 0 & 0 & -4.37085349142E-11-4.53336927688E-11*I \\ 0 & 0 & 3.32471067492E-12-1.00000000000E-12*I \end{matrix}$ (the second column are the interesting ones, they serve as coefficients for the powerseries in x for the expression {I,x}^^I ), and if x=1 they simply must be summed ) And the partial-sums of the second column should converge to y=I, since this means y = {I,1}^^I, : $\hspace{24} \begin{matrix} {rrr} 0.977995110024+0.146699266504*I \\ 0.570308500749+1.47507813506*I \\ -0.114402540375+1.14713275303*I \\ -0.0106044591818+0.993956473385*I \\ -0.00229741633360+1.00160960663*I \\ -0.000143765522959+0.999877073257*I \\ -0.0000575116782223+1.00002476990*I \\ -0.000000580602181001+1.00000205224*I \\ -0.00000100453146370+1.00000024808*I \\ -0.00000000833987995204+1.00000016631*I \\ 0.00000000258190521640+1.00000000353*I \\ -0.000000000512676097081+1.00000000285*I \\ 0.000000000486292953022+1.00000000023*I \\ 2.59309575160E-11+0.999999999974*I \\ 4.18678540668E-12+1.00000000000*I \\ 1.17217031429E-12+0.999999999999*I \\ 1.00000000000*I \\ 1.00000000000*I \\ 1.00000000000*I \\ 1.00000000000*I \\ 1.00000000000*I \\ 1.00000000000*I \\ 1.00000000000*I \\ 1.00000000000*I \end{matrix}$ This is also good for integer powers of this matrix; but again, for fractional or even complex powers the obtainable results for this parameters with that number of terms (24(last document) or 32) are not convincing. Gottfried Gottfried Helms, Kassel Matt D Junior Fellow Posts: 7 Threads: 3 Joined: Oct 2007 10/15/2007, 04:52 PM Wow, thanks everyone! --- just give me a second to digest it all... « Next Oldest | Next Newest »

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