“On the eighth day there shall be an assembly for you.”
– Numbers 29:35
The Sfas Emes conveys an insight, that "it is for you because the gates of teshuva are open to all. But Israel takes greater joy in accepting G-d’s service anew than they did in having their sins forgiven” (p.372, The Language of Truth). So, in light of this commentary, it may be conjectured, that while the focus of Rosh Hashannah was on repentance, and the Day of Yom Kippur on forgiveness, for Shemini Atzeret, a holiday that is connected to Simchas Torah, the focus is on renewal.