How do I show that the following functions are orthogonal?

Question

P0 = exp(-x/sqrt(2))
P1 = x*exp(-x/sqrt(2))
P2 = (x^2-1)*exp(-x/sqrt(2))

L^2 (-inf,inf)

Answer 1

Functions are said to be 'orthogonal on an interval' if the integral of their product over the interval is zero.

So do integral from -∞ to +∞ of P0*P1, etc. and show that they're all zero.


Doug

Answer 2

to show that two functions are orthogonal on an interval, we multiply the two functions together and integrate the result over the interval. If they are orthogonal, the integration of the product over the interval of interest is 0.

Answer 3

Do a convolution intergral between pairs of functions.