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## Homework Statement

The function f(x) = xe

^{-3x2}is expressed as a linear combination of the basis functions u

_{n}(x), which are orthogonal and normalised from minus infinity to infinity.

It is expressed by xe

^{-3x2}= ∑a

_{n}u

_{n}(x)

the u

_{n}(x)'s are even functions of x for n = 0,2,4 and are odd functions of x for n = 1,3,5

Calculate a

_{0}, a

_{1}and a

_{2}given that:

u1(x) = (4sqrt(2)/sqrt(pi))

^{1/2}xe

^{-x2}

I'm also told that the integral from -infinity to infinity of x

^{2}e

^{-a2x2}dx = sqrt(pi)/2a

^{3}

## Homework Equations

I'm aware of Gram Schmidt orthogonalisation but am at a bit of a loss as to how to do it from the second term and how to guess the next terms. I get the process but don't you need a set of linearly independent functions to do it to?

## The Attempt at a Solution

It's asking for the various coefficients and not the u(x) terms, but do I have to work those out with G-S orthogonalisation? If so I need to find the set of LI functions to orthogonalise.

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