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Computation and Experimental Evaluation of Mordell–Tornheim–Witten Sum Derivatives

ABSTRACT In the previous work, the present authors and others have studied Mordell–Tornheim–Witten sums and their connections with multiple-zeta values. In this note, we describe the numerical computation of derivatives at zero of a specialization originating in a preprint by Romik and the experimental evaluation of these numerical values in terms of well-known constants.