/bhavatu- / भवतुॱ

The pronoun nounbase "bhavatu" means "you".

/bhavatu- is grammatically third person (ISO meaning "you"). The third person goes with all titles that show respect. So instead of saying with a second person verb —

zRnu rAjan शृनु राजन् "please listen, your majesty"

you may use third person verbs with an honorific, like this —

zRnotu rAjA शृनोतु राजा "may your majesty listen"

zRnotu bhavAn शृनोतु भवान् "may your honor listen"

In old times /bhavatu- used to be a respectful form of address, like "your honor". Nowadays mostly everybody is addressed as /bhavatu-, I'd say.

/bhavatu- is a perfectly normal /matup base, like **hanumat- हनुमत्. So, when masculine, it sounds exactly like /bhavatR- "that is".

/bhavatu- + /am → !**bhavantam भवन्तम् " o you'" like **hanumantam हनुमन्तम्

bhavatu भवतु + /bhis → !**bhavadbhis भवद्भिस् "by you'''"

bhavatu भवतु + /zas → **bhavatas भवतस् " o you'''"

/bhavatR- + /am → bhavantam भवन्तम् " o who is"

bhavatu भवतु + /bhis → **bhavadbhis भवद्भिस् "by they who are"

bhavatu भवतु + /zas → **bhavatas भवतस् " o they who are"

The exception to that is non-/sambuddhi /su —

**bhavat'- भवत्ऽॱ m (with /matup) + /su → !**bhavAn भवान् "you", same steps as **hanumAn हनुमान्

**bhavat- भवत् (with /zatR) + /su → **bhavan भवन् "that is", same steps as **hasan हसन्

In the feminine, "you" is bhavatI- भवतीॱ and "she who is" is bhavantI- भवन्तीॱ.