# An asymptotic series for the digamma function

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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Do you know that other famous asymptotic series, by Stirling? Might there be a connection to this one? –  Gerald Edgar May 7 '12 at 13:39