Newton-Cotes integration for approximating Stieltjes (generalized Euler) constants
Newton-Cotes integration for approximating Stieltjes (generalized Euler) constants
In the Laurent expansion \[ \zeta (s,a)=\frac {1}{s-1}+\sum _{k=0}^{\infty }\frac {(-1)^{k} \gamma _{k}(a)}{k!} (s-1)^{k}, \text {\ \ } 0<a\leq 1,\] of the Riemann-Hurwitz zeta function, the coefficients $\gamma _{k}(a)$ are known as Stieltjes, or generalized Euler, constants. [When $a=1$, $\zeta (s,1)=\zeta (s)$ (the Riemann zeta function), and $\gamma _{k}(1)=\gamma _{k}$.] …