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?
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? 


We can prove this, using EulerMaclaurin 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. ^_^ 

