- #1
Perturbation
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Hey, this is a pretty simple induction problem, but I suck at induction and I think I'm missing something really obvious here, though trying to figure it out whilst having a pretty bad cold isn't much of a good idea.
The identity
[tex]\frac{1}{A_1\cdots A_n}=\int_0^1 dx_1\cdots dx_n \delta (\sum_i^nx_i-1) \frac{(n-1)!}{[A_1x_1+\cdots +A_nx_n]^n}[/tex]
Can be proven inductively, given that we know it works for n=2, by the use of
[tex]\frac{1}{AB^n}=\int^1_0 dxdy \delta (x+y-1)\frac{ny^{n-1}}{[Ax+By]^{n+1}}[/tex]
I get to a certain point then just can't see what to do. Gargh...
The identity
[tex]\frac{1}{A_1\cdots A_n}=\int_0^1 dx_1\cdots dx_n \delta (\sum_i^nx_i-1) \frac{(n-1)!}{[A_1x_1+\cdots +A_nx_n]^n}[/tex]
Can be proven inductively, given that we know it works for n=2, by the use of
[tex]\frac{1}{AB^n}=\int^1_0 dxdy \delta (x+y-1)\frac{ny^{n-1}}{[Ax+By]^{n+1}}[/tex]
I get to a certain point then just can't see what to do. Gargh...
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