An asymptotic series for the digamma function - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-21T23:48:11Z http://mathoverflow.net/feeds/question/96207 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/96207/an-asymptotic-series-for-the-digamma-function An asymptotic series for the digamma function Lwins.Gafield 2012-05-07T12:04:18Z 2012-05-07T14:19:45Z <p>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.</p> <p>How to make a proof?</p> http://mathoverflow.net/questions/96207/an-asymptotic-series-for-the-digamma-function/96218#96218 Answer by Lwins.Gafield for An asymptotic series for the digamma function Lwins.Gafield 2012-05-07T14:19:45Z 2012-05-07T14:19:45Z <p>We can prove this, using Euler-Maclaurin Formula. Here is a introduction from Wikipedia. <a href="http://en.wikipedia.org/wiki/Euler%E2%80%93Maclaurin_formula" rel="nofollow">http://en.wikipedia.org/wiki/Euler%E2%80%93Maclaurin_formula</a></p> <p>This is a quite easy problem. To Admin, You may be able to consider deleting this question, thanks. ^_^</p>