I want to compute the indefinite integral $$ \int \frac{\log\Gamma(\frac{x}{2})}{x^2}\,dx, $$ but fail myself. Do you know how to compute this integral?
2026-04-09 05:47:46.1775713666
Indefinite integral $ \int \frac{\log\Gamma(\frac{x}{2})}{x^2}\,dx$
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By Weirstrass formula , $$\log \Gamma(x)=-\gamma x-\log(x)+\sum_{n=1}^{\infty}\left( \frac{x}{n}-\log\left( 1+\frac{x}{n}\right) \right).$$