Welcome to mathimatikoi.org forum; Enjoy your visit here.

Digamma and Trigamma series

Calculus (Integrals, Series)
Post Reply
User avatar
Tolaso J Kos
Posts: 864
Joined: Sat Nov 07, 2015 6:12 pm
Location: Larisa

Digamma and Trigamma series


Post by Tolaso J Kos »

Let $\psi^{(0)}$ and $\psi^{(1)}$ denote the digamma and trigamma functions respectively. Prove that:

\[\sum_{n=1}^{\infty} \left ( \psi^{(0)}(n) - \ln n + \frac{1}{2} \psi^{(1)}(n) \right ) = 1+ \frac{\gamma}{2} - \frac{\ln 2\pi}{2}\]

where $\gamma$ denotes the Euler – Mascheroni constant.
Imagination is much more important than knowledge.

Post Reply

Who is online

Users browsing this forum: No registered users and 1 guest