I have a spherical harmonic which is a function of .I recently found an equation which is written as follows: .I am trying to understand its meaning in order to include it in my simulations. Note that in my case so the vectors become 2-dimensional.I know that in order to evaluate a Spherical Harmonic we need a value for and a value for .As I can understand from the equation above, the term will produce a new normalized vector, that is the difference between .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 , in steps of 0.1. My problem is that I want to evaluate the Spherical Harmonic for all the values of but I cannot see how to do it since the input to the spherical harmonic is the angle . Knowing that does not tell me anything about or DOES IT???
I would appreciate someone's help