# Integral equality

Integral equality....

let be a and b real numbers..and let be the integral...

$$\int_{-\infty}^{\infty}dxf(x)x^{a}\int_{-\infty}^{\infty}g(x+y)y^{ib}=0$$ so if this is zero also will be its conjugate:

$$\int_{-\infty}^{\infty}dxf(x)x^{a}\int_{-\infty}^{\infty}g(x+y)y^{-ib}=0$$ now let,s suppose we would have that (1-a,-b) is also a zero so:

$$\int_{-\infty}^{\infty}dxf(x)x^{1-a}\int_{-\infty}^{\infty}g(x+y)y^{-ib}=0$$ then my conclusion is that 1-a=a a=1/2 and there is no other solution.. :zzz:

shmoe