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That is not a polynomial. Polynomials only have their variables as basic terms with non-negative integer powers. If you have e^x where x is one of the variables then the expression is never a polynomial.
You appear to have F on both the left and right. Is that intended to be a recursive definition? If so then is the expression
F(t) = 2 * 1 / F(exp(t/tr1) + exp(-t/tr2))
or is it
F(t) = 2 * F[1 / (exp(t/tr1) + exp(-t/tr2)))
Either one is going to be non-trivial to find the expanded form, and there is a good chance that both tr1 and tr2 found would be complex.