Section: New Results
Computing Stieltjes constants using complex integration
Participant : Fredrik Johansson.
In , F. Johansson and I. Blagouchine devise an efficient algorithm to compute the generalized Stieltjes constants to arbitrary precision with rigorous error bounds, for the first time achieving this with low complexity with respect to the order . The algorithm consists of locating an approximate steepest descent contour and then evaluating the integral numerically in ball arithmetic using the Petras algorithm with a Taylor expansion for bounds near the saddle point. An implementation is provided in the Arb library.