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Significance of orthogonal polynomials

  1. Aug 26, 2013 #1
    Two polynomials are considered orthogonal if the integral of their inner product over a defined interval is equal to zero... is that a correct and complete definition? From what I understand, orthogonal polynomials form a basis in a vector space. Is that the desirable quality of orthogonal polynomials? Do they have any other additional properties that set them apart?
     
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  3. Aug 26, 2013 #2

    rcgldr

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  4. Aug 26, 2013 #3
    Thanks rcgldr. Is it safe to say that orthogonal polynomials are continuous?
     
  5. Aug 26, 2013 #4

    AlephZero

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    All polynomials are continuous functions :smile:

    But there are non-polynomial orthogonal functions which are not continuous, for example Haar and Walsh functions.
     
  6. Aug 26, 2013 #5
    Great!!! Thanks AlephZero! :smile:
     
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