I am trying to find out whether there is any difference in equations but I am not capable to find any information about Geoda equations and to try to compare them with ArcGis equations.
Thats a good question. I'm not certain but I think that the results should be the same since the derivation of these statistics are well established. What could be the difference, if any, I suspect is the precision of the data types used to generate results. I'd be interested in hearing more from the community on this question.
First I agree with John. It is a matter of implementation. Most software vendors hide such information; however the results are 'supposed' to be largely consistent.
Maybe the two software packages handle feature boundaries in a slightly different way. This has happened before with the ArcGIS K-Function which produced different results for "highly" irregular boundaries.
I also find they are different. When using k-nearest neighbors spatial matrix, the difference will increase as the 'k' increasing. I guess this is because of projected coordinate system. However, which one is correct?