Orthogonal polynomial

  • Thread starter sniffer
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  • #1
sniffer
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i am still learning mathematical physics.

i am learning orthogonal polynomials, but still confused.

what is the meaning of "orthogonal" here?
 

Answers and Replies

  • #2
Timbuqtu
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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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