• The Inria's Research Teams produce an annual Activity Report presenting their activities and their results of the year. These reports include the team members, the scientific program, the software developed by the team and the new results of the year. The report also describes the grants, contracts and the activities of dissemination and teaching. Finally, the report gives the list of publications of the year.

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Section: New Results

Computing Stieltjes constants using complex integration

Participant : Fredrik Johansson.

In [32], F. Johansson and I. Blagouchine devise an efficient algorithm to compute the generalized Stieltjes constants ${\gamma }_{n}\left(a\right)$ to arbitrary precision with rigorous error bounds, for the first time achieving this with low complexity with respect to the order $n$. 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.