Let $a_n$,$n=0,1,2...$ are real numbers.$f(x)=a_0+a_1x+a_2x^2...$ is a real power series with radius of convergence $R>0$. Suppose there exist $M>0$ such that for all real $x$ with $|x|
Bounded power series
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power-series
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0I don't understand what you mean about $\log$. Whether or not the coefficients are complex depends on where you do the expansion. Since the principal branch of $\log$ is real on the positive real line, any power series on the positive real line will have real coefficients. – 2012-12-13
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Hint: What is the power series for $\dfrac{1}{1+x^2}$?