Is there any relevant difference between ajjhupekkhati and upekkhati?
I’m very interested to know the nuances of this myself, as I’m not sure how upekkha in 3rd and 4th jhana functions exactly. Presumably the same as upekkha-bodhi-anga (awakening factor). And then, how does that differ from upekkha as a brahmavihara?
The typical explantion of “looking on equanimously” doesn’t quite give a complete picture I suspect.
upekkhati = upa + ikkhati
ajjhupekkhati = adhi + upa + ikkhati
Ikkhati [fr. īkṣ] to look J v.153; ThA 147; DhsA 172.
Upekkhati [upa + īkṣ] to look on, to be disinterested or indifferent Sn 911; Nd1 328; J vi.294.
Ajjhupekkhati [adhi + upa + ikṣ; cp. BSk. adhyupekṣati] 1. to look on A i.257; Miln 275.
to look on intently or with care, to oversee, to take care of A iv.45 (kaṭṭhɔaggi, has to be looked after); PvA 149 (sisaŋ colaŋ vā).
to look on indifferently to be indifferent to neglect Vin ii.78 = iii.162, cp. J i.147; M i.155 ii.223; A iii.194, 435; J v.229; DhA iv.125.
Yes, the same.