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MathGroup Archive 2007

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Re: How to express continued sum?

  • To: mathgroup at
  • Subject: [mg73456] Re: How to express continued sum?
  • From: "dimitris" <dimmechan at>
  • Date: Sat, 17 Feb 2007 05:01:31 -0500 (EST)
  • References: <er3hbm$f9e$>


Sum[f[x, y, z], {z, 0, 20}, {y, 0, 20}, {x, 0, 20}]

what do you want?


"Sum[f, {i, imax}] evaluates the sum of the expressions f as evaluated
for each i from 1 to imax. Sum[f, {i, imin, imax}] starts
with i = imin. Sum[f, {i, imin, imax, di}] uses steps di. Sum[f, {i,
imin, imax}, {j, jmin, jmax}, ... ] evaluates a sum over multiple
Attributes[Sum] = {HoldAll, Protected, ReadProtected}

Note also the presence of NSum


"NSum[f, {i, imin, imax}] gives a numerical approximation to the sum
of the expressions f as evaluated for each i from imin to \
imax. NSum[f, {i, imin, imax, di}] uses a step di in the sum."
Attributes[NSum] = {HoldAll, Protected}
Options[NSum] = {AccuracyGoal -> Infinity, Compiled -> True,
EvaluationMonitor -> None, Method -> Automatic,
     NSumExtraTerms -> 12, NSumTerms -> 15, PrecisionGoal ->
Automatic, VerifyConvergence -> True,
     WorkingPrecision -> MachinePrecision, WynnDegree -> 1}

By the way what language is this:
sigma(x=0..20)sigma(y=0..20)sigma(z=0..20)f(x,y,z)  ???


=CF/=C7 oicqgogogo at =DD=E3=F1=E1=F8=E5:
> I want to know how to get the continued sum expression by mathematica?
> Such
> as:
> sigma(x=0..20)sigma(y=0..20)sigma(z=0..20)f(x,y,z)
> Thanks!

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