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Tommy-Mandelbrot function - tommy1729 - 04/21/2015

Let a(x) = x^2 +1
Let b(x) be the functional inverse of a(x).
Let c(x) = x^2 +1 - exp(-2x).

D(x) = b^[n]( c^[1/2] (a^[n](x)) )
Where n Goes to infinity.

D(x) is the Tommy-Mandelbrot function.

Conjecture :

D(z) is analytic for Re(z) > 0 and z no element of the mandelbrot set from a(x).