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 picturing method. tommy1729 Ultimate Fellow Posts: 1,370 Threads: 335 Joined: Feb 2009 07/02/2014, 12:27 PM (This post was last modified: 07/02/2014, 08:00 PM by tommy1729.) The bottom side represents the real valued part of sexp*(x) where the domain is [0,3]. The range is thus [sexp*(0),sexp*(3)]. sexp*(x) is the ordinary sexp but with sexp(0) = 0. We assume strictly rising here. This part is estimated by a truncated real Taylor series with alternating signs. Now the upper left side is then sexp*(ix). the upper right side is exp^[3](sexp*(ix)) = sexp*(ix + 3). The diagonal has lenght 3sqrt(2) and is computed by continuation of sexp*(ix) and taking sexp*((-1)^{1/4} x). Now the red triangle has contour 0 ( because of cauchy's integral theorem ). Therefore all sides are defined thus solvable. Ofcourse we also require On the bottom side : sexp*(1) = 1 , sexp*(2) = e , On the diagonal side sexp*(i+1) = exp(sexp*(i)) , sexp*(2i+2) = exp(exp(sexp*(2i))). Now we can solve the equations and then pick one that satisfies sexp*(z+1) = exp(sexp*(z)). regards tommy1729 « Next Oldest | Next Newest »

 Messages In This Thread picturing method. - by tommy1729 - 07/02/2014, 08:30 AM RE: picturing method. - by tommy1729 - 07/02/2014, 12:27 PM RE: picturing method. - by tommy1729 - 07/02/2014, 08:14 PM RE: picturing method. - by tommy1729 - 07/02/2014, 09:00 PM RE: picturing method. - by tommy1729 - 07/03/2014, 08:23 AM

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