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 fake id(x) for better 2sinh method. tommy1729 Ultimate Fellow Posts: 1,419 Threads: 345 Joined: Feb 2009 06/04/2014, 11:10 PM (This post was last modified: 06/04/2014, 11:16 PM by tommy1729.) Wait a sec , it seems carlson's theorem applies here ! id(z) must grow fast enough otherwise id(z) - z is "close" to 0 for integer z , hence to avoid id(z) being flat it seems id(z) must grow fast enough in the imaginary direction. The problem is " close " is not the exact condition of the theorem (exactly 0 is). To make ln(id(z)/z) an entire function this also suggests id(z) is of exp type. Hence I write id(z) = z exp(t(z)) where t(z) is a taylor series. Now id(z)/z IS NEVER ALLOWED TO BE EQUAL TO 1. and exp(t(x)) for real x is a fake id(1) function. Thus t(x) is a fake id(0) function. However saying t(z) = id(z) - z brings us back to the Original problem ... Hmm. This is getting stranger by the sec. Maybe t(z) should be a fake id(0) for reals and a fake exp^[1/2](z) in the upper half plane ( in terms of absolute value ). But that brings us back again to carlson so I guess its better to have f(z) = fake id(0) around the real axis. f(z) = fake exp(z) near the imag axis. I finally see less objections. But what is f(z) ? regards tommy1729 « Next Oldest | Next Newest »

 Messages In This Thread fake id(x) for better 2sinh method. - by tommy1729 - 05/20/2014, 12:27 PM RE: fake id(x) for better 2sinh method. - by tommy1729 - 06/04/2014, 10:14 PM RE: fake id(x) for better 2sinh method. - by tommy1729 - 06/04/2014, 10:33 PM RE: fake id(x) for better 2sinh method. - by tommy1729 - 06/04/2014, 11:10 PM RE: fake id(x) for better 2sinh method. - by tommy1729 - 06/04/2014, 11:21 PM RE: fake id(x) for better 2sinh method. - by tommy1729 - 06/05/2014, 08:21 AM

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