As we know, there is an asymptotic series for the digamma function when $z>0$ is a real number. $$ \psi(z)=\ln z+\sum_{n=1}^{\infty}{\frac{B_n}{nz^n}} $$ $B_n$ is the first Bernoulli numbers.
How to make a proof?
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$\begingroup$ Do you know that other famous asymptotic series, by Stirling? Might there be a connection to this one? $\endgroup$– Gerald EdgarCommented May 7, 2012 at 13:39
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1 Answer
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We can prove this, using Euler-Maclaurin Formula. Here is a introduction from Wikipedia. http://en.wikipedia.org/wiki/Euler%E2%80%93Maclaurin_formula
This is a quite easy problem. To Admin, You may be able to consider deleting this question, thanks. ^_^