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 exp^[1/2](x) uniqueness from 2sinh ? tommy1729 Ultimate Fellow Posts: 1,493 Threads: 356 Joined: Feb 2009 06/03/2014, 09:51 PM A possible uniqueness critertion for exp^[1/2](x) ? For x > 1 and any integer n >= 0 : 1) e/n! > d^n exp^[1/2](x)/d^n x @ x = 1 > 0. 2) 2sinh^[1/2](x) + d 2sinh^[1/2](x)/dx - exp(-x) > exp^[1/2](x) > 2sinh^[1/2](x). ( 2sinh^[1/2](x) is computed with the koenigs function ) 3) exp^[1/2](z) is holomorphic for Re(z) > 1/2. If the uniqueness fails the question is if the conditions are too strong or too weak. And if it can be improved. regards tommy1729 tommy1729 Ultimate Fellow Posts: 1,493 Threads: 356 Joined: Feb 2009 06/03/2014, 09:58 PM Hmm The conditions must fail because they imply that exp^[1/2](x) is entire which it is not. Not sure how to bound the derivatives then ... reduce condition 1) to d^n exp^[1/2](x)/d^n x @ x = 1 > 0 ? regards tommy1729 « Next Oldest | Next Newest »

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