Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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:
    ([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
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted

Similar Threads - Orthogonality Relationship Legendre Date
I Orthogonality of spherical Bessel functions Jun 13, 2016
A Bessel decomposition for arbitrary function Apr 19, 2016
Orthogonality of Hermite functions Nov 12, 2014
Simple Integration Orthogonal Sin Nov 21, 2013
The significance of orthogonal relationships Jul 10, 2007