I'm looking into spherical harmonics, and the term 'order' seems to be used quite inconsistently.
In google's spherical harmonics framework (https://github.com/google/spherical-harmonics), the constant spherical harmonic is called order 0 so the total number of coefficients is (order + 1)^2
In NVIDIA's "Efficient Spherical Harmonics Evaluation" (http://jcgt.org/published/0002/02/06/) the constant spherical harmonic is called order 1, so the total number of coefficients is order^2
In the wikipedia article about spherical harmonics (https://en.wikipedia.org/wiki/Spherical_harmonics) the order can be negative and positive and describes the 'horizontal' index, with all zonal spherical harmonics being order 0.
Obviously there doesn't seem to be consensus about this - but can someone argue for one of them being the most proper use of the term 'order' in regards to spherical harmonics and why?