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Let $c=f(0)$ be a real number and $n,m$ positive integers. Let $P_k(n)$ be integer polynomials of $n$.

Let $f(n)$ be defined by the recursion $\left[\sum_{k=0}^{m} P_k(n)f(n+k)\right]+P_{-1}(n)=0$.

If $$\lim_{n\to\infty}\frac{f(n+1)}{f(n)} = 1$$ How does one compute $\lim_{n\to\infty}$ $\ln(f(n))/\ln(n)$ ?

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@nbubis: thanks for the edit. – mick Jan 22 '13 at 20:33
Still no answers after 11 months. – mick Jan 1 '14 at 21:49

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