Services & Resources / Wolfram Forums / MathGroup Archive
-----

MathGroup Archive 2012

[Date Index] [Thread Index] [Author Index]

Search the Archive

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.



  • Prev by Date: Writing a .3ds, getting an error from BinaryWrite
  • Next by Date: Re: Plotting colorfunctions over multiple parametric curves
  • Previous by thread: Writing a .3ds, getting an error from BinaryWrite
  • Next by thread: Can I solve this system of nonlinear equations?