Feynman Parameters: Solving an Induction Problem

[Perturbation]

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

$$\frac{1}{A_1\cdots A_n}=\int_0^1 dx_1\cdots dx_n \delta (\sum_i^nx_i-1) \frac{(n-1)!}{[A_1x_1+\cdots +A_nx_n]^n}$$

Can be proven inductively, given that we know it works for n=2, by the use of

$$\frac{1}{AB^n}=\int^1_0 dxdy \delta (x+y-1)\frac{ny^{n-1}}{[Ax+By]^{n+1}}$$

I get to a certain point then just can't see what to do. Gargh...

 

[Palindrom]

Well, whatever it is, I can't really see the more relevant parts of your post... The identity and the hint.
Maybe you should edit and add it at the end until Tex decides to work again.

 

[CarlB]

Put $$y = A_1A_2...A_{n-1}$$, it falls right out.

Carl

 

[athlonmp]

You can find the identity:
$$\frac{1}{A\*B^n}=...$$
useful

 

[zounnouf]

http://www.physics.thetangentbundle.net/wiki/Quantum_field_theory/Schwinger-Feynman_parameters

 

[zounnouf]

Or better :

http://theoretical-physics.net/dev/src/math/feynman-parameters.html

Then they explain more precisely what happens to the limits of the integrals.