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Inner product

  1. Jan 5, 2007 #1
    Hello, I am working on an assignment were I have shown that a certain equation defines an inner product, which was simple enough. Te equation was:

    [tex] \left\langle {f,g} \right\rangle = \int\limits_0^1 {f\left( x \right)g\left( x \right)x^2 dx} [/tex]

    My question then is: How do i state an equation for the inner product of x^p and x^q.

    Sorry if the information is sparse
    Last edited: Jan 5, 2007
  2. jcsd
  3. Jan 5, 2007 #2

    matt grime

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    You set f(x)=x^p and g(x)=x^q.
  4. Jan 5, 2007 #3


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    Looks straight forward to me. If
    [tex]<f,g>= \int_0^1 f(x)g(x)x^2 dx[/tex]
    f(x)= xp, and g(x)= xq, then
    [tex]<f,g>= \int_0^1 (x^p)(x^q)x^2dx= \int_0^1 x^{p+q+2}dx[/tex]
  5. Jan 5, 2007 #4


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    And you can give an exact number equal to that last expression.
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