Let
Li2(z)=∞∑n=1znn2.
This polylogarithm satisfies the following Abel identity:
Li2(−x)+logxlogy+Li2(−y)+log(1+yx)logy+Li2(−1+yx)+log(1+yx)log(1+x+yxy)+Li2(−1+x+yxy)+log(1+xy)log(1+x+yxy)+Li2(−1+xy)+log(1+xy)logx=−π22.
The following function
ELin,m(x,y,q)=∞∑j=1∞∑k=1xjjnykkmqjk
is defined in
the paper in (2.1).
Are there some known identities similar to the Abel identity for ELin,m(x,y,q)? Thank you very much.
This post imported from StackExchange MathOverflow at 2017-02-18 11:07 (UTC), posted by SE-user Jianrong Li