- #1
Mike706
- 51
- 0
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.
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.
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