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Orthogonal polynomial

  1. Jul 18, 2005 #1
    i am still learning mathematical physics.

    i am learning orthogonal polynomials, but still confused.

    what is the meaning of "orthogonal" here?
     
  2. jcsd
  3. Jul 18, 2005 #2
    Orthogonality of two elements of a vectorspace (in this case the space of all polynomials) is only defined with respect to an inner product on the space. A possible inner product on a polynomial space could for instance be:

    [tex] \left<f,g\right>= \int_0^1 f(x) g(x) dx[/tex]

    Now f and g are orthogonal [tex]\iff \left<f,g\right>=0[/tex].

    A set of polynomials is called orthogonal if each polynomial is orthogonal to each other polynomial in the set.
     
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