BQN's arithmetic functions use mostly the same symbols as APL, and the functionality is actually defined by the language implementation's number system and not the specification, so there's not too much to say about them.
Summary of differences for APLers:
⋆, since asterisk * is rendered inconsistently across fonts and sometimes appears as a superscript.√.¬, and logical functions (described on their own page) are extended linearly in all arguments instead of using GCD or LCM.