I am currently working on python script that does Hartree-Fock-Calculations. I try to avoid packages as good as possible. I've figured out how to calculate the one electron integrals when it comes to the Roothaan-Hall-Equations through this paper. I am now stuck however at calculating the two electron integrals. I've gathered that there are several recursive methods one can use since the analytical methods are quite inefficient for the vast amount of integrals that are needed to be calculated. I am however struggling with figuring out which algorithm is best for my problem and where to find literature on that. I am using a STO-3G basis set and maybe a 6-31G one. There are no shells that surpass an angular-momentum quantum number of 2.
Therefore my question is: What algorithm is the best for a closed shell molecule when I'm using a STO-3G / 6-31G basis set? Can you provide me with literature that is at least somewhat easy to understand?