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

zbMATH Open1283.11124arXiv1110.3493MaRDI QIDQ446301

Kohji Matsumoto, Hirofumi Tsumura

Publication date: 5 September 2012

Published in: Moscow Journal of Combinatorics and Number Theory (Search for Journal in Brave)

Abstract: 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.

Full work available at URL: https://arxiv.org/abs/1110.3493

zbMATH Keywords

double zeta valuesdouble L-valuesdouble polylogarithmssum formulas

Mathematics Subject Classification ID

Other Dirichlet series and zeta functions (11M41) Multiple Dirichlet series and zeta functions and multizeta values (11M32)

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