Evaluating a Complex Function

Algebra Level 4

Consider the function f(x)=11x2 f(x)=\frac {1} {\sqrt {1-x^2} } which is defined for all complex numbers apart from 1 and -1. f(2011)(15)f^{(2011)} ( \frac {1} {5} ) has the form abc \frac {a\sqrt{b}} {c} , where aa and c c are coprime integers and b b is not divisible by the square of any prime. What is the value of a+b+c a + b +c ?

Details and assumptions

f(n)(x) f^{(n)} (x) means that f f is applied n n times, e.g. f(2)(x)=ff(x)=f(f(x))f^{(2)} (x) = f \circ f (x) = f( f( x) )

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