nested sums

*To*: mathgroup at smc.vnet.net*Subject*: [mg125219] nested sums*From*: Severin Pošta <severin at km1.fjfi.cvut.cz>*Date*: Wed, 29 Feb 2012 07:26:19 -0500 (EST)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com

I have noticed that Sum[x^a y^b z^c, {a, 0, Infinity}, {b, 0, Infinity}, {c, 0, a - b}] produces "wrong" result (-y + z - y z + x y z)/((-1 + x) (-1 + y) (y - z) (-1 + x z)) because a-b is not checked to be nonnegative in the nested sums. This is probably by design (?). I wonder if I can achieve such check to be perfomed. This does not work: Sum[x^a y^b z^c If[a - b >= 0, 1, 0], {a, 0, Infinity}, {b, 0, Infinity}, {c, 0, a - b}] This also does not work: Sum[x^a y^b z^c Piecewise[{{1, a - b >= 0}}], {a, 0, Infinity}, {b, 0, Infinity}, {c, 0, a - b}] It is also interesting that Sum[...,{},{}] is not equivalent to Sum[Sum[...,{}],{}]. The following produces correct result: s= Sum[x^a y^b z^c Piecewise[{{1, a - b >= 0}}], {c, 0, a - b}]; s1=Sum[s, {b, 0, Infinity}]; Sum[s1,{a, 0, Infinity}] -(1/((-1 + x) (-1 + x y) (-1 + x z))) Interesting. S.