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.

KEYWORDS:

• Mordell-Tornheim-Witten sums
• PSLQ algorithm
• high-precision computation

2000 AMS SUBJECT CLASSIFICATION:

• 01A70
• 11Y60
• 11Y70

Acknowledgments

D. H. Bailey wishes to thank Karl Dilcher and an anonymous referee for valuable comments in the preparation of this document.