I have a spherical harmonic which is a function of Y_{nm}(\theta,\phi) .I recently found an equation which is written as follows: Y_{nm}(\frac{x_2 - x_1}{\left\|x_2 - x_1\right\|}).I am trying to understand its meaning in order to include it in my simulations. Note that in my case \theta = \pi/2 so the vectors become 2-dimensional.I know that in order to evaluate a Spherical Harmonic we need a value for \theta and a value for \phi.As I can understand from the equation above, the \frac{x_2 - x_1}{\left\|x_2 - x_1\right\|}term will produce a new normalized vector, that is the difference between x_2 - x_1.In my case the points/vectors are located on a circle (not inside the circle) of some radius R.
The author of the book mentions that the magnitude is \left\|x_2 - x_1\right\| = 0.1,0.2,...2, in steps of 0.1. My problem is that I want to evaluate the Spherical Harmonic for all the values of \left\|x_2 - x_1\right\| = 0.1,0.2,...2 but I cannot see how to do it since the input to the spherical harmonic is the angle (\theta=\pi/2, \phi). Knowing that \left\|x_2 - x_1\right\| = 0.1,0.2,...2does not tell me anything about x_2 - x_1 or DOES IT???

I would appreciate someone's help