Sum formulas for double polylogarithms with a shifting parameter and their derivatives

Details Sum formulas for double polylogarithms with a shifting parameter and their derivatives Sum formulas for double polylogarithms with a shifting parameter and their derivatives

2011-10-16

arxiv.org/abs/1110.3493v1

Mathematics

Number Theory

17 pages

Scientific paper

We prove sum formulas for double polylogarithms of Hurwitz type, that is, involving a shifting parameter $b$ in the denominator. These formulas especially imply well-known sum formulas for double zeta values, and sum formulas for double $L$-values. Further, differentiating in $b$, we obtain a kind of weighted sum formula for double polylogarithms and double $L$-values. We also give sum formulas for partial double zeta values with some congruence conditions. Our proofs of those sum formulas are based on certain functional relations for double polylogarithms of Hurwitz type.

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