Bug introduced in V10.0.2 or earlier and persists through V11.3
(Simplified version - courtesy Lukas Lang - reported [CASE:4208776])
I try to compute
Sum[2^Max[0, 2 h - b - c - 2] x^b y^c z^(2 h), {h, \[Infinity]}, {b, h}, {c, h}]
and get
(-y z^2 - x y z^2 + x^4 y z^2 + 4 y z^4 + 6 x y z^4 + 3 x^2 y z^4 + x^3 y z^4
- 4 x^4 y z^4 - 2 x^5 y z^4 + 2 y^2 z^4 + 3 x y^2 z^4 + 2 x^2 y^2 z^4 + x^3 y^2 z^4
- 2 x^4 y^2 z^4 - x^5 y^2 z^4 - 8 x y z^6 - 8 x^2 y z^6 - 4 x^3 y z^6 - x^4 y z^6
+ 8 x^5 y z^6 - 8 y^2 z^6 - 16 x y^2 z^6 - 14 x^2 y^2 z^6 - 10 x^3 y^2 z^6 + 6 x^4 y^2 z^6
+ 8 x^5 y^2 z^6 + 2 x^6 y^2 z^6 - 2 x y^3 z^6 - 3 x^2 y^3 z^6 - 2 x^3 y^3 z^6
+ 2 x^5 y^3 z^6 + 4 x^4 y z^8 + 16 x y^2 z^8 + 24 x^2 y^2 z^8 + 20 x^3 y^2 z^8
+ 10 x^4 y^2 z^8 - 16 x^5 y^2 z^8 - 8 x^6 y^2 z^8 + 8 x y^3 z^8 + 16 x^2 y^3 z^8
+ 14 x^3 y^3 z^8 + 4 x^4 y^3 z^8 - 8 x^5 y^3 z^8 - 4 x^6 y^3 z^8 - 8 x^4 y^2 z^10
- 16 x^2 y^3 z^10 - 24 x^3 y^3 z^10 - 16 x^4 y^3 z^10 + 16 x^6 y^3 z^10)
/(x (-1 + 4 z^2) (-1 + 2 x z^2) (-1 + 2 y z^2) (-1 + x y z^2))
This cannot be correct since the input is symmetric in x
and y
while the output is not.
At the same time
Sum[2^Max[0, 2 h - b - c - 2] x^b y^c z^(2 h), {h, 2, \[Infinity]}, {b, h}, {c, h}]
seems to sum up correctly.
Is there some known bug or I am doing something wrong?
Sum[2^Max[0, 2 h - b - c - 2] x^b y^c z^(2 h), {b, h}, {c, h}]/.h->1
is already broken $\endgroup$ – Lukas Lang Jan 2 '19 at 19:11