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Can anyone help me?

Q. An inner product is defined on the vector space V of all (real) polynomials (of arbitrary

degree) by

<f,g>=Int(x*e^(-x)*f(x)*g(x),x=o..infinity

Show that the linear differential operator

L=-x*(d^2/dx^2)-(2-x)*(d/dx):V->V

is symmetric with respect to this inner product.

Don't necessarily need the exact answer, just need to know how I'm meant to go about it.

Q. An inner product is defined on the vector space V of all (real) polynomials (of arbitrary

degree) by

<f,g>=Int(x*e^(-x)*f(x)*g(x),x=o..infinity

Show that the linear differential operator

L=-x*(d^2/dx^2)-(2-x)*(d/dx):V->V

is symmetric with respect to this inner product.

Don't necessarily need the exact answer, just need to know how I'm meant to go about it.

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