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How to create an expression of a N-fold integration?

C Z
Posted 11 years ago

Hi, I wonder whether it is possible to set a k-fold integration, where k is a variable?enter image description here Take the equation in the attachment for example. It doesn't have to "solve" it because I don't think in general, it is able to unless the function in the integration is very nice. But at least, I would like to have an expression that mathematica can treat it as a function of k. Is this possible?

POSTED BY: C Z
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C Z
C Z
Posted 11 years ago

Thanks, Nasser. Could you explain a little bit of the Plus @@ and Sequance @@? I searched but didn't find any clue about them.

POSTED BY: C Z

you could try

  foo[t_, n_] := Module[{s, z},
    z = Array[t, n];
    s = (Plus @@ (z[[2 ;; n - 1]])) (g[Sequence @@ z]/(z[[n]] + z[[1]]));
    Integrate[s, Sequence @@ ({#, 0, Infinity} & /@ z)]
    ]

For example

  Grid[Table[{k, foo[t, k]}, {k, 3, 6}], Alignment -> Left]

enter image description here

You can change the indexing as needed.
POSTED BY: Nasser M. Abbasi
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