On generalized gamma functions related to the Laurent coefficients of the Riemann zeta function
The paper discusses a class of generalized gamma functions \(\Gamma_ k (z)\), defined as a generalization of Euler's limit for the gamma function. The paper concentrates on the numbers \(\gamma_ k\) which, on the one hand, appear as coefficients in the Laurent expansion of the Riemann zeta function at the point 1, and on the other hand as the coefficient of the linear term in the Maclaurin expansion in \(\ln \Gamma_ k(z)\) at \(z=0\). A new series expansion for \(\gamma_ k\) is derived and these and related constants are numerically computed for \(1\leq k\leq 15\).
scientific article; zbMATH DE number 636043