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Orthogonality Relationship for Legendre Polynomials in Cylindrical Coordinates

  1. Dec 7, 2011 #1
    Hello everyone,

    Sorry if this is in the wrong sub-forum, I wasn't sure exactly where to place it.

    I was wondering if there is an orthogonality relationship for the Legendre polynomials P[itex]^{0}_{n}[/itex](x) that have been converted to cylindrical coordinates from spherical coordinates, similar to the form where P[itex]^{0}_{n}(x)[/itex]P[itex]^{0}_{m}(x)[/itex] is integrated from x = -1 to x = 1.

    By converted to cylindrical coordinates from spherical, I mean that originally x is taken as:
    cos([itex]\varphi[/itex])
    ([itex]\varphi[/itex] being the angle between the z axis and the position vector (from the solution to Laplace's equation)),
    and cos([itex]\varphi[/itex]) is replaced by [itex]\frac{z}{\sqrt{r^{2}+z^{2}}}[/itex].

    Thanks, I appreciate the help.
     
    Last edited: Dec 7, 2011
  2. jcsd
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