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Conjecture about the equality : $f(y)=y\ln(y)+\sum_{n=2}^{\infty}\pm\frac{\left(y\ln y\right)^n}{2^{a_n}}$

Such as a $y$ might exist but its VERY specific to that choice of $y$ if we try to analyze the function generally we won't find any such magic set of coefficients. So we start with $f(x) = \frac{\left(...

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