I want to proof the series of kummer. Therefore I want to show $$2 \cdot \int_0^1 \log\big(\Gamma(x)\big) \cdot \sin(2 \pi n x) dx = \frac{\gamma + \log(2 \pi) + \log(n)}{n \pi},$$ where $\gamma$ is the Euler-Mascheroni-constant.

Any help would be appreciated. Thanks in advance.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.