At the following circuit I want to find what it does and basically its transfer function. I've searched a lot but I didn't find any circuit like this. Since it does not match any of the basic types of op amp circuits (inverting or non-inverting amplifier) I don't know where to start from. Finally, anyone knows what's the name of this circuit? Please note that this is not homework.
Following Lorenzo Donati's method I got to this point for the transfer function: