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 sandbox conjecture tommy1729 Ultimate Fellow Posts: 1,365 Threads: 333 Joined: Feb 2009 06/13/2011, 05:47 AM consider a(x) and b(x). both functions are real-analytic. both functions are entire. both functions are strictly increasing on the reals. a(0) > 0 , b(0) > 0 a(x) has exactly 2 positive real fixpoints : lower fixpoint A < 1 and upper fixpoint B > 1 b(x) has exactly 2 positive real fixpoints : lower fixpoints A < 1 and upper fixpoint B > 1 a(x) = b(x) has only 2 finite real solutions : their commen fixpoints. ** sandbox conjecture ** let c(x) = a(b(x)) and d(x) = b(a(x)) if sum k = 0 , oo (-1)^k a^k(1) has the same value as its corresponding matrix method - sum of elements in second line of 1/(1 + carleman(a(x))) ) - and if sum k = 0 , oo (-1)^k b^k(1) has the same value as its corresponding matrix method and if sum k = 0 , oo (-1)^k c^k(1) has the same value as its corresponding matrix method then sum k = 0 , oo (-1)^k d^k(1) has the same value as its corresponding matrix method. tommy1729 « Next Oldest | Next Newest »

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