We provide an efficient method to evaluate the generalized Stieltjes constants $\gamma_n(a)$ numerically to arbitrary accuracy for large $n$ and $n \gg |a|$ values. The method uses an integral representation for the constants and evaluates the integral by applying the double exponential (DE) quadrature method near the saddle points of the integrands. Further, we provide a highly accurate asymptotic formula for the generalized Stieltjes constants.

翻译：我们提供了一种有效的方法,用数字和任意的精确度来评价大额美元和大额美元和大额美元的总和Stieltjes常数的数值。该方法对常数采用整体表示法,并在先祖的马鞍点附近应用双倍指数(DE)二次方位法来评价整体。此外,我们为普遍使用的Stieltjes常数提供了非常准确的平衡公式。