MathOverflow is a question and answer site for professional mathematicians. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

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?

share|cite|improve this question
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
up vote 2 down vote accepted

We can prove this, using Euler-Maclaurin Formula. Here is a introduction from Wikipedia.

This is a quite easy problem. To Admin, You may be able to consider deleting this question, thanks. ^_^

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.