\int dz G[z,y]^n J[z] [/itex] vs. (\int dz G[z,y] J[z])^n

[wandering.the.cosmos]

If one is given two known functions G[x,y] and J[y], is there an explicit transformation that could be constructed to give us either one of the following integrals from the other?

[tex] \int dz G[z,y]^n J[z] [/itex]
[tex] \left( \int dz G[z,y] J[z] \right)^n [/itex]

Here n is an integer.

Thanks!

 

[Gib Z]

Ahh made tex won't work in titles, better name it integrals or something. I would imagine that transformation is not possible, but I don't know.

 

[AlphaNumeric]

I would imagine not because it's not too hard to come up with G and J which give your first integral as divergent over particular domains for certain n and your second one well defined.

 

[wandering.the.cosmos]

I would imagine not because it's not too hard to come up with G and J which give your first integral as divergent over particular domains for certain n and your second one well defined.

This means the transformation doesn't exist in all generality. But I'd be interested in such a transformation even for restricted classes of G and J.