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To apply a transformation

  1. Oct 2, 2006 #1
    I wish to expand

    [tex]f(x) = 1 - \frac{x^2}{4} , -2 \leq x \leq 2 [/tex]

    in terms of Legendre polynomials.

    I know that the transformation

    [tex]u = \frac{x}{2}[/tex]

    maps the function onto the interval (-1,1), but how do I apply this transformation?

    Should I use

    [tex]g(x) = uf(x)[/tex]

    or maybe

    [tex]g(x) = f(u(x))[/tex]

  2. jcsd
  3. Oct 2, 2006 #2


    User Avatar
    Science Advisor

    g(x)= f(u(x)). You are basically making a "change of variable".
  4. Oct 2, 2006 #3
    But shouldn't [tex]f(2) = g(1)[/tex]?
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