Hill
Hill[x, y]
gives the Hill identity with arguments x
and y
. The returned object is 0
.
See also
Overview, SimplifyPolyLog.
Examples
Hill[a, b]
% /. a :> .123 /. b :> .656 // Chop
Li2(1−b1−a)+Li2(ab)−Li2(a(1−b)(1−a)b)+log(a)(log(1−a)−log(1−b))+log(1−b1−a)(−log(aa−b)+log(1−ba−b)−log(a)+log(1−b))−(−log(aa−b)+log(a(1−b)a−b)+log(1−b))log(a(1−b)(1−a)b)+Li2(a)−Li2(b)−6π2
0
Hill[x, x y] // PowerExpand // SimplifyPolyLog // Expand
% /. x :> .34 /. y -> .6 // N // Chop
ζ(2)−Li2(xy)+Li2(1−xy1−x)−Li2(1−xy(1−x)y)−Li2(1−x)−Li2(1−y)−log(x)log(1−xy)−log(1−y)log(y)
0