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2023-01-16T04:42:39Z
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Sum formulas for double polylogarithms with a shifting parameter and their derivatives
Matsumoto, Kohji
Tsumura, Hirofumi
open access
double zeta values
double polylogarithms
double L-values
sum formulas
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.
Moscow Institute of Physics and Technology
2011-12-29
eng
journal article
VoR
http://hdl.handle.net/2237/20428
https://nagoya.repo.nii.ac.jp/records/18326
http://mjcnt.phystech.edu/en/article.php?id=35
2220–5438
Moscow Journal of Combinatorics and Number Theory
1
4
58
79
https://nagoya.repo.nii.ac.jp/record/18326/files/16.pdf
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385.7 kB
2018-02-21