 2 fixpoint pairs  - Printable Version +- Tetration Forum (https://math.eretrandre.org/tetrationforum) +-- Forum: Tetration and Related Topics (https://math.eretrandre.org/tetrationforum/forumdisplay.php?fid=1) +--- Forum: Mathematical and General Discussion (https://math.eretrandre.org/tetrationforum/forumdisplay.php?fid=3) +--- Thread: 2 fixpoint pairs  (/showthread.php?tid=959) 2 fixpoint pairs  - tommy1729 - 02/18/2015 A general question. Let A(z) be a transcendental real-entire function without real fixpoints. Let I(z) be the functional inverse of A(z). I(z) has no singularities for Re(z) > 0. I(z) = z has exactly 2 conjugate pair solutions. The fixpoints of I(z) are all repelling and have real part > 0. Also they have the same derivative. (up to conjugate) Then by using the Kneser method we can find 2 real-analytic superfunctions based on one of the fixpoint pairs of I(z). By using analytic one-periodic theta functions we can modify those 2 superfunctions such that they are bounded in the strip 0 < Re(z) < 1. Call these real-analytic superfunctions F(z) and G(z). Consider D = lim F(z-n)/G(z-n) Im intrested in the behaviour of F(z) / ( D G(z) ) - 1 in the complex plane. regards tommy1729