Formules relatives à la fonction \(\varGamma\). (French) JFM 52.0358.01

Ser, J.

Nouv. Ann. de Math. (6) 1, 385-386 (1926).

Beweis der Formel \[ \log \frac{\varGamma(x+a)}{\varGamma(a)} = x \frac{\varGamma^\prime(a)}{\varGamma(a)} + \frac{P_2}{a} + \frac{1! \, P_3}{a(1+a)} + \cdots, \] wo \[ P_{n+1} = \int_0^x \frac{x(1-x) \dots (n-1-x)}{n!} \, dx. \]

Reviewer: Grunsky, H., Dr. (Berlin)